Cohomological properties of simple complexes of groups

A simple complex of groups is a functor from a poset to the category of groups satisfying certain properties. They were introduced by Bridson and Haefliger as an abstract way to encode isotropy subgroups of actions on posets. A simplex complex of groups which embeds in a group $K$ has an associated $K$-poset. We will explain how to obtain information about the classifying space of $K$ through the $K$-equivariant homotopy type of the construction of Bridson-Haefliger, and we will also obtain finiteness properties of cohomology.