Motivic homotopy theory of group scheme actions

Abstract

We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish homotopical purity and blow-up theorems for finite abelian groups.Comment: Final version, to appear in Journal of Topology. arXiv admin note: text overlap with arXiv:1403.191