  We apply results of Harada, Holm and Henriques to prove that the Atiyah-Segal
equivariant complex $K$-theory ring of a divisive weighted projective space
(which is singular for nontrivial weights) is isomorphic to the ring of
integral piecewise Laurent polynomials on the associated fan. Analogues of this
description hold for other complex-oriented equivariant cohomology theories, as
we confirm in the case of homotopical complex cobordism, which is the universal
example. We also prove that the Borel versions of the equivariant $K$-theory
and complex cobordism rings of more general singular toric varieties, namely
those whose integral cohomology is concentrated in even dimensions, are
isomorphic to rings of appropriate piecewise formal power series. Finally, we
confirm the corresponding descriptions for any smooth, compact, projective
toric variety, and rewrite them in a face ring context. In many cases our
results agree with those of Vezzosi and Vistoli for algebraic $K$-theory,
Anderson and Payne for operational $K$-theory, Krishna and Uma for algebraic
cobordism, and Gonzalez and Karu for operational cobordism; as we proceed, we
summarize the details of these coincidences.
