The equivariant KK-theory of toric varieties

This paper contains two results concerning the equivariant KK-theory of toric varieties. The first is a formula for the equivariant KK-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this result is established in a more general context, involving the KK-theory of graded projective modules. The second result is a new proof of a theorem due to Vezzosi and Vistoli concerning the equivariant KK-theory of smooth (not necessarily affine) toric varieties.