  Any finite simplicial complex K and a partition of the vertex set of K
determines a canonical quotient space of the moment-angle complex of K. We
prove that the cohomology groups of such a space can be computed via some
Hochster's type formula, which generalizes the usual Hochster's formula for the
cohomology groups of moment-angle complexes. In addition, we show that the
stable decomposition of moment-angle complexes can also be extended to such
spaces. This type of spaces include all the quasitoric manifolds that are
pullback from the linear models. And we prove that the moment-angle complex
associated to a finite simplicial poset is always homotopy equivalent to one of
such spaces.
