An Eilenberg-Ganea Phenomenon for Actions with Virtually Cyclic   Stabilisers
  In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological dimension is 2 while the Bredon geometric dimension is 3. 
Martin Fluch and Ian J. Leary
math.GR math.GT