Completion theorem for equivariant $K$-theory
  In this paper, we study the algebraic analogue of the topological Atiyah-Segal completion theorem. We verify this completion theorem for the algebraic equivariant $K$-theory of smooth projective schemes. We also show that the completion theorem fails in general for smooth non-projective schemes. 
Amalendu Krishna
math.AG math.KT