  Toric orbifolds are a topological generalization of projective toric
varieties associated to simplicial fans. We introduce some sufficient
conditions on the combinatorial data associated to a toric orbifold to ensure
the existence of an invariant cell structure on it and call such a toric
orbifold retractable. In this paper, our main goal is to study equivariant
cohomology theories of retractable toric orbifolds. Our results extend the
corresponding results on divisive weighted projective spaces.
