  In this article we describe the $T_{comp}$-equivariant topological $K$-ring
of a $T$-{\it cellular} simplicial toric variety. We further show that
$K_{T_{comp}}^0(X)$ is isomorphic as an $R(T_{comp})$-algebra to the ring of
piecewise Laurent polynomial functions on the associated fan denoted
$PLP(\Delta)$. Furthermore, we compute a basis for $K_{T_{comp}}^0(X)$ as a
$R(T_{comp})$-module and multiplicative structure constants with respect to
this basis.
