Motivic Tambara Functors

Abstract: Let k be a field and denote by SH(k) the motivic stable homotopy category. Recall its full subcategory HI_0(k) of effective homotopy modules. Write NAlg(HI_0(k)) for the category of normed motivic spectra with underlying spectrum an effective homotopy module. In this article we provide an explicit description of NAlg(HI_0(k)) as the category of sheaves with generalized transfers and \'etale norms, and explain how this is closely related to the classical notion of Tambara functors.