We present a simple model for characters of irreducible representations of
semi-simple Lie groups and, more generally, for Demazure characters. This is
a combinatorial counterpart of the Littelmann path model. We give an explicit
combinatorial Chevalley-type formula for equivariant K-theory of generalized
flag manifolds G/B. The construction is given in terms of alcove paths, which
correspond to decompositions of affine Weyl group elements, and saturated
chains in the Bruhat order on the usual Weyl group. A key ingredient is
a certain R-matrix that satisfies the Yang-Baxter equation.
This is joint work with Cristian Lenart.