This talk is a report on joint work with Jeremiah Heller and Paul Arne Østvær. The Gabber-Gillet-Thomason rigidity theorem asserts that the natural map from a Henselian local ring to its residue field induces an isomorphism on algebraic K-theory with finite coefficients (coprime to the exponential characteristic). We establish a version of this rigidity theorem in the setting of homotopy invariant equivariant pseudo pretheories of smooth schemes over a field with an action of a finite group. Examples include equivariant algebraic K-theory and presheaves with equivariant transfers.
