Equivariant $K$-theory of smooth projective spherical varieties
  We present a description of the equivariant $K$-theory of a smooth projective spherical variety. This provides an integral $K$-theory version of Brion's calculation of equivariant Chow-cohomology of such varieties. We consider the equivariant $K$-theory of wonderful compactifications of minimal rank symmetric varieties. We obtain a formula for their structure constants in terms of certain lower dimensional Schubert classes. This generalizes results of Uma on equivariant compactifications of adjoint groups. 
S. Banerjee and Mahir Bilen Can
math.KT