In this paper, we define an action of the group of equivariant Cartier
divisors on a toric variety X on the equivariant cycle groups of X, arising
naturally from a choice of complement map on the underlying lattice. If X is
nonsingular, this gives a lifting of the multiplication in equivariant
cohomology to the level of equivariant cycles. As a consequence, one naturally
obtains an equivariant cycle representative of the equivariant Todd class of
any toric variety. These results extend to equivariant cohomology the results
of Thomas and Pommersheim. In the case of a complement map arising from an
inner product, we show that the equivariant cycle Todd class obtained from our
construction is identical to the result of the inductive, combinatorial
construction of Berline-Vergne. In the case of arbitrary complement maps, we
show that our Todd class formula yields the local Euler-Maclarurin formula
introduced in Garoufalidis-Pommersheim.Comment: 15 pages, to be published in Michigan Mathematical Journal; LaTe
