Equivariant K-theory of affine flag manifolds and affine Grothendieck polynomials

Abstract

We study the equivariant $K$-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variety in the K-group is represented by a unique polynomial, which we call the affine Grothendieck polynomial