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We construct for an equivariant homology theory for proper equiv- ariant CW-complexes an equivariant Chern 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 Qn Z KnORGU and Qn Z LnORGU for a commutative ring R with QH R, provided the Farrell-Jones Conjecture with respect to F is true, and of QnZ K top n ˇ C r OG; FU for Fa R; C, provided the Baum-Connes Conjecture is true.

Chern characters for proper equivariant homology theories and applications to K - and L -theory