The Galois‐equivariant K$K$‐theory of finite fields

Abstract We compute the ‐graded equivariant algebraic ‐groups of a finite field with an action by its Galois group . Specifically, we show these ‐groups split as the sum of an explicitly computable term and the well‐studied ‐graded coefficient groups of the equivariant Eilenberg–MacLane spectrum . Our comparison between the equivariant ‐theory spectrum and further shows they share the same Tate spectra and geometric fixed point spectra. In the case where has prime order, we provide an explicit presentation of the equivariant ‐groups.