EQUIVARIANT MOTIVIC HOMOTOPY THEORY

Abstract. In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here will be compared to those by Voevodsky and Hu-Kriz-Ormsby. We show that our model struc-ture allows to detect equivariant motivic weak equivalences on fixed points and how this property also leads to a topologically convenient behavior of stable equivalences. We also prove a negative result concerning descent for equivariant algebraic K-theory. 1