Title: Equivariant vector bundles over classifying spaces for 
proper actions 

Authors:  Dieter Degrijse and Ian J Leary 

Affiliations: Degijse: 
Centre for Symmetry and Deformation, University of Copenhagen 
Leary: University of Southampton 

Abstract: 
We give the first examples of discrete groups G for which there exist
compatible collections of representations over the finite subgroups of
G that do not come from any G-equivariant (virtual) vector bundle on
the classifying space for proper actions of G.  This implies that the
Atiyah-Hirzebruch spectral sequence for computing the equivariant
topological K-theory of the classifying space for proper actions of G
has non-zero differentials.  We show that this cannot happen for
right-angled Coxeter groups, and we compute K-theory for these groups.