Orbifold Hodge Numbers of Calabi-Yau Hypersurfaces

We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h_{orb}^{1,1}$ and $h_{orb}^{n-2,1}$ for the hypersurface. We give applications to the orbifold string theory conjecture and orbifold mirror symmetry.