2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61880We 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 $h^{1,1}_{orb}$ and $h^{n-2,1}_{orb}$ for the hypersurface. We give applications to the orbifold string theory conjecture and orbifold mirror symmetry.LaTeX, 25 PagesAlgebraic Geometry14E15,14J32,53C80text