Recent advances in computational techniques for K-theory allow us to
describe the K-theory of toric varieties in terms of the K-theory of
fields and simple cohomological data. The cohomological data consists
of the cyclic homology and the cdh-cohomology of Kähler differentials.
As an application, we give a new proof of Gubeladze's Dilation Theorem,
which verifies his "nilpotence conjecture" for the action of dilations
on the K-theory of toric varieties.