Witt vectors and Tambara functors

Abstract

We give a combinatorial description of the ring of G-Witt vectors on a polynomial algebra over the integers for every finite group G. Using this description we show that the functor, which takes a commutative ring with trivial action of G to its ring of Witt vectors, coincides with the left adjoint of the algebraic functor from the category of G-Tambara functors to the category of commutative rings with an action of G.