Le Gall, Pierre-Yves Equivariant Kasparov theory and groupoids. I. (Théorie de Kasparov équivariante et groupoïdes. I.) (French) Zbl 0932.19004 \(K\)-Theory 16, No. 4, 361-390 (1999). The content of the paper is part of the author’s thesis. The main results have been announced [P.-Y. Le Gall, C. R. Acad. Sci., Paris, Sér. I 324, No. 6, 695-698 (1997; Zbl 0883.46041)]. Motivated by the work of M. Hilsum and G. Skandalis [Ann. Sci. Éc. Norm. Supér., Sér. IV 20, 325-390 (1987; Zbl 0656.57015)] on foliations and aiming at proofs of the Novikov and of the Baum-Connes conjectures for foliations the author extends Kasparov’s equivariant \(KK\)-theory from actions of groups to actions of groupoids. He establishes the existence of the product and of functoriality properties with respect to morphisms of groupoids. Reviewer: H.Schröder (Dortmund) Cited in 4 ReviewsCited in 47 Documents MSC: 19K35 Kasparov theory (\(KK\)-theory) 46L80 \(K\)-theory and operator algebras (including cyclic theory) 22A22 Topological groupoids (including differentiable and Lie groupoids) 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) 58J22 Exotic index theories on manifolds Keywords:Kasparov theory; equivariant \(KK\)-theory; groupoids Citations:Zbl 0883.46041; Zbl 0656.57015 PDFBibTeX XMLCite \textit{P.-Y. Le Gall}, \(K\)-Theory 16, No. 4, 361--390 (1999; Zbl 0932.19004) Full Text: DOI