B. Ammann, R. Lauter, and V. Nistor, Pseudodifferential operators on manifolds with a Lie structure at infinity, vol.165, pp.717-747, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00098401

B. Ammann, R. Lauter, and V. Nistor, On the geometry of Riemannian manifolds with a Lie structure at infinity, Int. J. Math. and Math. Sciences, vol.4, pp.161-193

I. Androulidakis and G. Skandalis, The analytic index of elliptic pseudodifferential operators on a singular foliation, J. K-Theory, vol.8, issue.3, pp.363-385, 2011.

M. F. Atiyah and I. M. Singer, The index of elliptic operators I, Ann. of Math, vol.87, issue.2, pp.484-530, 1968.

P. Baum and R. Douglas, of Proceedings of Symposia in Pure Mathematics, vol.38, pp.117-173, 1982.

P. Baum, R. Douglas, and K. , Operator algebras and K-theory, pp.1-31, 1981.

P. Baum, N. Higson, and T. Schick, On the equivalence of geometric and analytic K-homology, Pure Appl. Math. Q, vol.3, issue.1, pp.1-24, 2007.

P. Baum, E. Van-erp, K. , F. Operators, and I. I. ,

K. Bohlen and E. Schrohe, Getzler rescaling via adiabatic deformation and a renormalized index formula, J. Math. Pures Appl

U. Bunke, Index theory, eta forms, and Deligne cohomology, Mem. Amer. Math. Soc, vol.198, issue.928, 2009.

U. Bunke, A K-theoretic relative index theorem and Callias-type Dirac operators, Math. Ann, vol.303, issue.2, pp.241-279, 1995.

P. Carrillo-rouse and J. M. Lescure, Geometric obstructions for Fredholm boundary conditions for manifolds with corners, Ann. K-Theory, vol.3, issue.3, pp.523-563, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01490931

P. Carrillo-rouse and B. L. Wang, Geometric Baum-Connes assembly map for twisted differentiable stacks, Ann. Sci. Éc. Norm. Supér, issue.4, pp.277-323, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02011004

A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part I, pp.521-628, 1982.

, A. Connes Connes, Alain. Noncommutative geometry, 1994.

C. Carvalho, V. Nistor, and Y. Qiao, Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebras, Electron. Res. Announc. Math. Sci, vol.24, pp.68-77, 2017.

M. Crainic and R. Fernandes, Integrability of Lie brackets, Ann. of Math, issue.2, pp.575-620, 2003.

C. Debord, Holonomy groupoids of singular foliations, J. Differential Geom, vol.58, issue.3, pp.467-500, 2001.

C. Debord and J. M. , Lescure, K-duality for stratified pseudomanifolds, Geom. Topol, vol.13, issue.1, pp.49-86, 2009.

C. Debord, J. Lescure, and V. Nistor, Groupoids and an index theorem for conical pseudo-manifolds, J. Reine Angew. Math, vol.628, pp.1-35, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00094949

C. Debord, J. M. Lescure, and F. Rochon, Pseudodifferential operators on manifolds with fibred corners, vol.65, pp.1799-1880, 2015.
DOI : 10.5802/aif.2974

URL : http://www.numdam.org/article/AIF_2015__65_4_1799_0.pdf

C. Debord and G. Skandalis, Blowup constructions for Lie groupoids and a Boutet de Monvel type calculus

C. Debord and G. Skandalis, Lie groupoids, exact sequences, Connes-Thom elements, connecting maps and index maps
DOI : 10.1016/j.geomphys.2018.03.012

H. Emerson and R. Meyer, Bivariant K-theory via correspondences, Adv. Math, vol.225, issue.5, pp.2883-2919, 2010.
DOI : 10.1016/j.aim.2010.04.024

URL : https://doi.org/10.1016/j.aim.2010.04.024

H. Emerson and R. Meyer, Dualities in equivariant Kasparov theory, New York J. Math, vol.16, pp.245-313, 2010.

M. Hilsum and G. Skandalis, Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov (d'après une conjecture d'A. Connes). (French) [[K-oriented morphisms of spaces of leaves and functoriality in Kasparov theory, Ann. Sci. École Norm. Sup, issue.4, pp.325-390, 1987.
DOI : 10.24033/asens.1537

URL : http://www.numdam.org/article/ASENS_1987_4_20_3_325_0.pdf

M. Karoubi, Classics in Mathematics, 2008.

R. Lauter, B. Monthubert, and V. Nistor, Pseudodifferential analysis on continuous family groupoids, Doc. Math, vol.5, pp.625-655, 2000.

R. Lauter and V. Nistor, Analysis of geometric operators on open manifolds: a groupoid approach. Quantization of singular symplectic quotients, Progr. Math, pp.181-229, 2001.

P. Gall, Théorie de Kasparov équivariante et groupoides. I. (French) [Equivariant Kasparov theory and groupoids. I], K-Theory, vol.16, pp.361-390, 1999.

P. Loya and R. Melrose, Fredholm perturbations of Dirac operators on manifolds with corners, 2003.

K. Mackenzie, General theory of Lie groupoids and Lie algebroids, vol.213, 2005.
DOI : 10.1017/cbo9781107325883

R. B. Melrose, Differential analysis on manifolds with corners

B. Monthubert, Groupoids and pseudodifferential calculus on manifolds with corners, J. Funct. Anal, vol.199, issue.1, pp.243-286, 2003.
DOI : 10.1016/s0022-1236(02)00038-1

URL : https://doi.org/10.1016/s0022-1236(02)00038-1

B. Monthubert and V. Nistor, A topological index theorem for manifolds with corners, Compos. Math, vol.148, issue.2, pp.640-668, 2012.
DOI : 10.1112/s0010437x11005458

URL : https://hal.archives-ouvertes.fr/hal-00007727

B. Monthubert and F. Pierrot, Indice analytique et groupoides de Lie, C. R. Acad. Sci. Paris Ser. I Math, vol.325, issue.2, pp.193-198, 1997.
DOI : 10.1016/s0764-4442(97)84598-3

P. S. Muhly, J. Renault, and D. P. Williams, Equivalence and isomorphism for groupoid C * -algebras, J. Operator Theory, vol.17, issue.1, pp.3-22, 1987.

V. Nistor, Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains, Contemp. Math, vol.366, pp.307-328, 2005.
DOI : 10.1090/conm/366/06734

V. Nistor, Desingularization of Lie groupoids and pseudodifferential operators on singular spaces
DOI : 10.4310/cag.2019.v27.n1.a5

URL : http://arxiv.org/pdf/1512.08613

V. Nistor, Analysis on singular spaces: Lie manifolds and operator algebras, J. Geom. Phys, vol.105, pp.75-101, 2016.
DOI : 10.1016/j.geomphys.2016.03.014

URL : https://hal.archives-ouvertes.fr/hal-01285202

V. Nistor, A. Weinstein, and P. Xu, Pseudodifferential operators on differential groupoids, Pacific J. Math, vol.189, issue.1, pp.117-152, 1999.

A. Paterson, Continuous family groupoids, Homology, Homotopy and Applications, vol.2, pp.89-104, 2000.

A. Savin, Elliptic operators on manifolds with singularities and K-homology, K-theory, vol.34, pp.71-98, 2005.

G. Skandalis, On the strong ext bifunctor, 1983.

S. Vassout, Unbounded pseudodifferential calculus on Lie groupoids, J. Funct. Anal, vol.236, issue.1, pp.161-200, 2006.

. Zenobi, Adiabatic groupoids and secondary invariants in K-theory