  Let $M$ be a symplectic toric manifold acted on by a torus $\mathbb{T}$. In
this work we exhibit an explicit basis for the equivariant K-theory ring
$\mathcal{K}_{\mathbb{T}}(M)$ which is canonically associated to a generic
component of the moment map. We provide a combinatorial algorithm for computing
the restrictions of the elements of this basis to the fixed point set; these,
in turn, determine the ring structure of $\mathcal{K}_{\mathbb{T}}(M)$. The
construction is based on the notion of local index at a fixed point, similar to
that introduced by Guillemin and Kogan in [GK].
  We apply the same techniques to exhibit an explicit basis for the equivariant
cohomology ring $H_{\mathbb{T}}(M; \mathbb{Z})$ which is canonically associated
to a generic component of the moment map. Moreover we prove that the elements
of this basis coincide with some well-known sets of classes: the equivariant
Poincar\'e duals to the closures of unstable manifolds, and also the canonical
classes introduced by Goldin and Tolman in [GT], which exist whenever the
moment map is index increasing.
