2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68160We compute explicitly the equivariant Hirzebruch $χ_y$-characteristic of an equivariant complex line bundle over a toric manifold and state a weighted version of the quantization commutes with reduction principle in symplectic geometry. Then, we give a weighted decomposition formula for any simple polytope in $\R^n$. This formula generalizes a polytope decomposition due to Lawrence [10] and Varchenko [14] and extends a previous weighted version obtained by Karshon, Sternberg and Weitsman [9].14 pages, 2 figures. Followed suggestions by referee and restructured all sections. Accepted for publicationSymplectic GeometryCombinatorics65B15 (Primary); 52B20, 53D20 (Secondary)text