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Two remarks about the Baum-Connes map. (Deux remarques sur l’application de Baum-Connes.) (French) Zbl 1003.46037
Summary: Let \(G\) be a locally compact Hausdorff group. The authors show in first part that a space endowed with a proper action of \(G\) is locally induced from spaces with an action of a compact subgroup of \(G\). As a consequence for the Baum-Connes map, the slice condition can be removed from the notion of proper action in the definition of the topological theory of a group. In a second part, they show that the Baum-Connes map for \(G\) with coefficients in a proper algebra is an isomorphism.

46L55 Noncommutative dynamical systems
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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