Almost equivariant maps for td-groups

Abstract

We construct certain maps from buildings associated to td-groups to a space closely related to the classifying numerable $G$-space for the family $\mathcal{C}\mathrm{vcy}$ of covirtually cyclic subgroups. These maps are used elsewhere to study the K-theory of Hecke algebras in the spirit of the Farrell–Jones conjecture.