Classifying spaces with virtually cyclic stabilizers for linear groups
  We show that every discrete subgroup of $\mathrm{GL}(n,\mathbb{R})$ admits a finite dimensional classifying space with virtually cyclic stabilizers. Applying our methods to $\mathrm{SL}(3,\mathbb{Z})$, we obtain a four dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic $K$-theory of its group ring. 
Dieter Degrijse, Ralf K\"ohl, Nansen Petrosyan
math.GR math.AT math.KT