The K-theoretic Farrell-Jones conjecture for a group G states that the map p:E_{VCYC}(G)\rightarrow \{\cdot\} induces an isomorphism on homology .
Here E_{VCYC}(G) denotes the classifying space of the group G with respect to the family of virtually cyclic subgroups, i.e. a G-CW-complex whose isotropy groups are virtually cyclic and for any virtually cyclic subgroup of G the fixed point set is contractible.