We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map $hocoli{m}_{{}_d}G/d(-)\to \left|W\right|$ which is a (non-equivariant) homotopy equivalence, hence $hocoli{m}_{{}_d}EG{\times }_G{F}_d\to EG{\times }_G\left|W\right|$ is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves...