Let X be a finite connected CW -complex. Suppose that its fundamental group π is residually finite, i.e., there is a nested sequence . . . ⊂ Γm+1 ⊂ Γm ⊂ . . . ⊂ π of in π normal subgroups of finite… (More)

We discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic K-theory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then… (More)

We construct for an equivariant homology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions are satis®ed. This applies for instance to the… (More)

This survey article is devoted to the Baum-Connes Conjecture about the topological K-theory of the reduced group C∗-algebra and the Farrell-Jones Conjecture about the algebraicKand L-theory of the… (More)

We prove a version of the Atiyah-Segal completion theorem for proper actions of an infinite discrete group G. More precisely, for any finite proper G-CW-complex X, K(EG×GX) is the completion of K ∗… (More)

We prove a version of the L2-index Theorem of Atiyah, which uses the universal center-valued trace instead of the standard trace. We construct for G-equivariant K-homology an equivariant Chern… (More)

We define for a topological group G and a family of subgroups F two versions for the classifying space for the family F , the G-CW -version EF (G) and the numerable G-space version JF (G). They agree… (More)

The verification of the isomorphism conjectures of Baum and Connes and Farrell and Jones for certain classes of groups is used to compute the algebraic Kand L-theory and the topologicalK-theory of… (More)

We first construct a classifying space for defining equivariant K-theory for proper actions of discrete groups. This is then applied to construct equivariant Chern characters with values in Bredon… (More)