Motivic homotopy theory of group scheme actions
  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. 
Jeremiah Heller, Amalendu Krishna, Paul Arne Ostvaer
math.AT math.AG