Chern characters for equivariant $K$-theory of proper $G$-CW-complexes
by Wolfgang L\"uck and Bob Oliver
AMS classification: primary 55N91, secondary 19L47
Addresses:
Institut f"ur Mathematik und Informatik
Westf"alische Wilhelms-Universit"at
Einsteinstr. 62
48149 M"unster, Germany
Laboratoire de Mathematiques
Universite Paris-Nord
Av. J-B Clement
93430 Villetaneuse, France
E-mail: lueck@math.uni-muenster.de, bob@math.univ-paris13.fr
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 cohomology with
coefficients in the representation ring functor $R(-)$ (tensored by the
rationals). And this in turn is applied to prove some versions of the
Atiyah-Segal completion theorem for real and complex $K$-theory of proper
actions of discrete groups.