Equivariant K-theory of cellular toric varieties

In this article we describe the Tcomp-equivariant topological K-ring of a T-{ cellular} simplicial toric variety. We further show that K_Tcomp⁰(X) is isomorphic as an R(Tcomp)-algebra to the ring of piecewise Laurent polynomial functions on the associated fan denoted PLP(Δ). Furthermore, we compute a basis for K_Tcomp⁰(X) as a R(Tcomp)-module and multiplicative structure constants with respect to this basis.