Chern characters for equivariant $K$-theory of proper $G$-CW-complexes
by Wolfgang L\"uck and Bob Oliver

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.