  Let X be a smooth projective variety with the action of the n dimensional
torus. The article describes the moduli space of torus equivariant morphisms
from stable toric varieties into X as the inverse limit of the GIT quotients of
X and their flips when these spaces are enhanced with a naturally associated
Deligne-Mumford stack structure. This description is used for constructing a
class in the Chow group of the moduli space of dimension dim(X)-n which is
invariant to equivariant deformations of X.
