Homotopy theory of $G$–diagrams and equivariant excision

Abstract

Let $G$ be a finite group. We define a suitable model-categorical framework for $G$–equivariant homotopy theory, which we call $G$–model categories. We show that the diagrams in a $G$–model category which are equipped with a certain equivariant structure admit a model structure. This model category of equivariant diagrams supports a well-behaved theory of equivariant homotopy limits and colimits. We then apply this theory to study equivariant excision of homotopy functors.