Chern characters for proper equivariant homology theories and applications to K- and L-theory, by W. Lueck

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 of finite subgroups and in the Baum-Connes Conjecture. Thus we get an explicit calculation of the rationalization of K_n(RG) and L_n(RG) for a commutative ring R which contains the rational numbers Q as subring, and of the rationalization of the topological K-groups K_n(C_r^*(G,F)) for F the real or complex numbers in terms of group homology, provided the Farrell-Jones Conjecture with respect to the family of finite subgroups resp. the Baum-Connes Conjecture is true.


W. Lueck <lueck@math.uni-muenster.de>