In a Hamiltonian torus action with isolated fixed points, every reduced space is cobordant to a disjoint union of toric varieties. These toric varieties carry a stable complex structure, incompatible with their symplectic structure. For a K¨ahler toric variety corresponding to a convex polytope ∆ it is known that the quantization corresponds to the lattice points in ∆. We generalize this result to the stable complex case.