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

We construct for an equivariant homology theory for proper equivariant CW -complexes an equivariant Chern character under certain conditions. 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 of Q ⊗Z Kn(RG) and Q ⊗Z Ln(RG) for a commutative ring R with Q ⊂ R and of Q ⊗Z K top n (C∗ r (G, F )) for F = R, C in terms of group homology, provided the Farrell-Jones Conjecture with respect to F resp. the Baum-Connes Conjecture is true.