  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 samples a comparison to the
one by Voevodsky and Hu-Kriz-Ormsby. We show that it allows to detect
equivariant motivic weak equivalences on fixed points and how this property
leads to a topologically convenient behavior of stable equivalences. We also
prove a negative result concerning descent for equivariant algebraic K-theory.
