  Let G be a discrete group for which the classifying space for proper
G-actions is finite-dimensional. We find a space W such that for any such G,
the classifying space PBG for proper G-bundles has the homotopy type of the
W-nullification of BG. We use this to deduce some results concerning PBG and in
some cases where there is a good model for PBG we obtain information about the
BZ/p-nullification of BG.
