Motivic spectral Mackey functors

Abstract

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the category of motivic G-spaces with finite \'etale transfers over X at the trivial representation sphere. Along the way we obtain several results of independent interest, among them: we construct and study norms in the motivic homotopy theory of stacks, and we extend the homotopy t-structure to DM-stacks and establish some favorable properties.