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.
"Equivariant $K$-theory of toric orbifolds." J. Math. Soc. Japan 73 (3) 735 - 752, July, 2021. https://doi.org/10.2969/jmsj/83548354