We construct for an equivariant homology theory for proper equivariant CW-complexes an equivariant Chem character, provided that certain conditions are satisfied. This applies for instance to the sources of the assembly maps in the Farrell-Jones Conjecture with respect to the family F of finite subgroups and in the Baum-Connes Conjecture. Thus we get an explicit calculation in terms of group homology of Q x(Z) K-n(RG) and Q x(Z) L-n(RG) for a commutative ring R with Q subset of R, provided the Farrell-Jones Conjecture with respect to F is true, and of Q x(Z) K-n(top) (C-r(*)(G, F)) for F = R, C, provided the Baum-Connes Conjecture is true. [References: 26]
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