  We study the GKM theory for a equivariant stratified space having orbifold
structures in tis successive quotients. Then, we introduce the notion of an
\emph{almost simple polytope}, as well as a \emph{divisive toric variety}
generalizing the concept of a divisive weighted projective space. We employ the
GKM theory to compute the generalized equivariant cohomology theories of toric
varieties associated to almost simple polytopes and divisive toric varieties.
