Toric Deligne–Mumford stacks and the better behaved version of the GKZ hypergeometric system

We generalize the combinatorial description of the orbifold (Chen–Ruan) cohomology and of the Grothendieck ring of a Deligne–Mumford toric stack and its associated stacky fan in a lattice N in the presence of a deformation parameter β ∈ N ⊗ ℂ. As an application, we construct a topological mirror symmetry map that produces a complete system of Γ-series solutions to the better behaved version of the GKZ hypergeometric system for β ∈ N ⊗ ℂ.