C. Anantharaman-delaroche, Amenability and exactness for dynamical systems and their C * -algebras, Transactions of the American Mathematical Society, vol.354, issue.10, pp.4153-4178, 2002.
DOI : 10.1090/S0002-9947-02-02978-1

URL : https://hal.archives-ouvertes.fr/hal-00076697

C. Anantharaman-delaroche and J. Renault, Amenable groupoids, Monographies de L'Enseignement Mathématique [Monographs of L, Enseignement Mathématique], vol.36, 2000.

A. Arveson, Notes on extensions of C * -algebras, Duke Math, J, vol.44, issue.2, pp.329-355, 1977.

P. Baum and A. Connes, Geometric K-theory for Lie groups and foliations, Enseign. Math, issue.2 12, pp.46-49, 2000.

E. Bédos, P. , and L. Harpe, Moyennabilité intérieure des groupes : définitions et exemples, Enseign. Math, vol.32, issue.2 12, pp.139-157, 1986.

B. Bekka, A. Pierre-de-la-harpe, and . Valette, A geometric description of equivariant K-homology for proper actions, Quanta of maths, Clay Math, New Mathematical Monographs, pp.1-22, 2008.

É. Blanchard, C. Déformations-de, and . Hopf, D??formations de $C\sp*$-alg??bres de Hopf, Bulletin de la Société mathématique de France, vol.124, issue.1, pp.141-215, 1996.
DOI : 10.24033/bsmf.2278

E. Blanchard, Subtriviality of continuous fields of nuclear C * -algebras, J. Reine Angew. Math, vol.489, pp.133-149, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00922873

P. Nathanial, N. Brown, and . Ozawa, C * -algebras and finite-dimensional approximations, Graduate Studies in Mathematics, vol.88, 2008.

M. Crainic and I. Moerdijk, Foliation Groupoids and Their Cyclic Homology, Advances in Mathematics, vol.157, issue.2, pp.177-197, 2001.
DOI : 10.1006/aima.2000.1944

URL : https://doi.org/10.1006/aima.2000.1944

]. A. Con82 and . Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part I, Proc. Sympos. Pure Math, pp.521-628, 1980.

[. Rouse, Indices analytiques à support compact pour les groupoïdes de lie, 2007.

P. Carrillo-rouse and B. Wang, Twisted longitudinal index theorem for foliations and wrong way functoriality [CS84] A. Connes and G. Skandalis, The longitudinal index theorem for foliations, Adv. Math. Publ. Res. Inst. Math. Sci, vol.226, issue.20 6, pp.4933-4986, 1984.

G. Edward and . Effros, Property ? and inner amenability, Proc. Amer, pp.483-486, 1975.

[. Ehresmann, Catégories et structures, 1965.

G. Goehle, Groupoid crossed products, ProQuest LLC
DOI : 10.1349/ddlp.263

URL : http://arxiv.org/pdf/0905.4681

[. Green, Equivariant K-theory and crossed product c * -algebras, Poc, Symposia Pure Math, vol.38, issue.13, pp.337-338, 1982.

J. Higson and . Roe, Amenable group actions and the Novikov conjecture, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.147, issue.519, pp.143-153, 2000.
DOI : 10.1515/crll.2000.009

M. Hilsum and G. Skandalis, Stabilit?? des $C^*$-alg??bres de feuilletages, Annales de l???institut Fourier, vol.33, issue.3, pp.201-208, 1983.
DOI : 10.5802/aif.936

M. Hilsum and G. Skandalis, Morphismes $K$-orient??s d'espaces de feuilles et fonctorialit?? en th??orie de Kasparov (d'apr??s une conjecture d'A. Connes), Annales scientifiques de l'??cole normale sup??rieure, vol.20, issue.3, pp.325-390, 1987.
DOI : 10.24033/asens.1537

K. Knudsen, J. , and K. Thomsen, Elements of KK-theory, Mathematics : Theory & Applications, 1991.

]. G. Kas80a and . Kasparov, Hilbert C * -modules : theorems of Stinespring and Voiculescu, J. Operator Theory, vol.4, issue.1, pp.133-150, 1980.

. [. Le and . Gall, Théorie de Kasparov équivariante et groupoïdes, C. R. Acad. Sci. Paris Sér. I Math, vol.324, issue.6, pp.695-698, 1997.

P. Gall, Théorie de Kasparov équivariante et groupoïdes. I, K-Theory, pp.361-390, 1999.

W. Lück and B. Oliver, The completion theorem in K-theory for proper actions of a discrete group, Topology, vol.40, issue.3, pp.585-616, 2001.
DOI : 10.1016/S0040-9383(99)00077-4

[. , M. Lau, and A. L. Paterson, Inner amenable locally compact groups, Trans. Amer. Math. Soc, vol.325, issue.1, pp.155-169, 1991.
DOI : 10.2307/2001664

URL : http://www.ams.org/tran/1991-325-01/S0002-9947-1991-1010885-5/S0002-9947-1991-1010885-5.pdf

W. Lück, Survey on Classifying Spaces for Families of Subgroups, Progr. Math, vol.248, pp.269-322, 2005.
DOI : 10.1007/3-7643-7447-0_7

[. Michael, Continuous selections. I, Ann. of Math, pp.361-382, 1956.
DOI : 10.1016/b978-044450355-8/50029-5

J. [. Moerdijk and . Mr?un, Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics, vol.91, 2003.
DOI : 10.1017/CBO9780511615450

]. J. Neu29 and . Neumann, Zur allgemeinen theorie des masses, Fundamenta Mathematicae, vol.13, issue.1, pp.73-116, 1929.

[. Ozawa, Amenable actions and exactness for discrete groups, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.330, issue.8
DOI : 10.1016/S0764-4442(00)00248-2

G. K. Pedersen, C * -algebras and their automorphism groups, 1979.

[. Pier, Amenable locally compact groups, Pure and Applied Mathematics, 1984.

J. Renault and B. Moran, Ideal structure of groupoid crossed product C * algebras , Miniconferences on harmonic analysis and operator algebras (Canberra, Proc. Centre Math, pp.267-268, 1987.

]. A. Sed76 and . Seda, Haar measures for groupoids, Proc. Roy. Irish Acad. Sect. A, vol.76, issue.5, pp.25-36, 1976.

[. Skandalis, Une Notion de nucl??arit?? en K-th??orie (d'apr??s J. Cuntz), K-Theory, vol.1, issue.6, pp.549-573, 1988.
DOI : 10.1007/BF00533786

[. Thomsen, Asymptotic Homomorphisms and EquivariantKK-Theory, Journal of Functional Analysis, vol.163, issue.2, pp.324-343, 1999.
DOI : 10.1006/jfan.1998.3377

URL : https://doi.org/10.1006/jfan.1998.3377

J. Tu, La conjecture de Baum???Connes pour les feuilletages moyennables, K-Theory, vol.17, issue.3, pp.215-264, 1999.
DOI : 10.1023/A:1007744304422

J. Tu, P. Xu, and C. Laurent-gengoux, Twisted K-theory of differentiable stacks, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.37, issue.6, pp.841-910, 2004.
DOI : 10.1016/j.ansens.2004.10.002

URL : https://hal.archives-ouvertes.fr/hal-00104608

A. Valette, Le rôle des fibrés de rang fini en théorie de Kasparov équivariante, Acad. Roy. Belg. Cl. Sci. Mém. Collect, vol.8, issue.2 6, p.45, 1988.

]. S. Vas01 and . Vassout, Feuilletages et résidu non commutatif longitudinal, 2001.

]. T. Wil93 and . Willmore, Riemannian geometry, 1993.

P. Dana, . E. Williamswin83-]-h, and . Winkelnkemper, Crossed products of C * -algebras The graph of a foliation, Mathematical Surveys and Monographs Ann. Global Anal. Geom, vol.134, issue.1 3, pp.51-75, 1983.

[. Yu, The coarse Baum???Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Inventiones mathematicae, vol.139, issue.1, pp.201-240, 2000.
DOI : 10.1007/s002229900032