The equivariant Steenrod algebra (Q1122183)

This paper presents a generalization of the mod p Steenrod algebra \(A^*\) to G-equivariant cohomology theory for a finite group G. The coefficient ring is an arbitrary minimal Mackey functor field \({\mathcal F}\). The equivariant Steenrod algebra graded on the real representation ring RO(G) is then defined as H\({\mathcal F}^*H{\mathcal F}\), where H\({\mathcal F}\) denotes the Eilenberg-MacLane G-spectrum associated to \({\mathcal F}\). It is shown that the computation of H\({\mathcal F}^*H{\mathcal F}\) reduces to \(HF^*HF\), where F is some Galois extension of the finite field \({\mathbb{Z}}/p\). To complete the computation, a description of the bimodule and Hopf algebra structures on \(HF^*HF\) in terms of the structures on \(A^*\) and Hom(F,F) is given.