Spaces of maps into classifying spaces for equivariant crossed complexes

We give an equivariant version of the homotopy theory of crossed complexes. The applications generalize work on equivariant Eilenberg—Mac Lane spaces, including the non abelian case of dimension 1, and on local systems. It also generalizes the theory of equivariant 2-types, due to Moerdijk and Svensson. Further, we give results not just on the homotopy classification of maps but also on the homotopy types of certain equivariant function spaces.