Equivariant $K$-theory of divisive torus orbifolds

TLDR: In this article, the concept of divisive torus orbifolds is introduced and a combinatorial description of equivariant K-theory for torus manifolds over acyclic polytopes is given.

Abstract: The category of torus orbifolds is a generalization of the category of toric orbifolds which contains projective toric varieties associated to complete simplicial fans. We introduce the concept of “divisive” torus orbifolds following divisive weighted projective spaces. The divisive condition may ensure an invariant cell structure on a locally standard torus orbifold. We give a combinatorial description of equivariant K-theory, equivariant cobordism theory and equivariant cohomology theory of divisive torus orbifolds. In particular, we get a combinatorial description of these generalize cohomology theories for torus manifolds over acyclic polytopes.