  Quasitoric spaces were introduced by Davis and Januskiewicz in their 1991
Duke paper. There they extensively studied topological invariants of quasitoric
manifolds.
  These manifolds are generalizations or topological counterparts of
nonsingular projective toric varieties. In this article we study structures and
invariants of quasitoric orbifolds. In particular, we discuss equivalent
definitions and determine the orbifold fundamental group, rational homology
groups and cohomology ring of a quasitoric orbifold. We determine whether any
quasitoric orbifold can be the quotient of a smooth manifold by a finite group
action or not. We prove existence of stable almost complex structure and
describe the Chen-Ruan cohomology groups of an almost complex quasitoric
orbifold.
