  We study Bredon homology approximations for spaces with an action of a
compact Lie group G. We show that if M is a coMackey functor satisfying mild
p-locality conditions, then Bredon homology of a G-space X with coefficients in
M is determined by fixed points of p-toral subgroups of G acting on X. As an
application we prove a vanishing result for the Bredon homology of the complex
L_n of direct-sum decompositions of complex n-space.
