With the use of Atiyah-Bott-Berline-Vergne formula in equivariant cohomology, we count lattice points in the moment polytope of a toric manifold with isolated fixed points. Lattice points are counted with weights depending on the codimension of the smallest dimensional face in the polytope that contains them. We derive a way of computing the equivariant Hirzebruch characteristic of a line bundle over a toric manifold and get, as a particular case, a weighted version of quantization commutes with reduction principle for toric manifolds. More generally, we obtain a polar decomposition of a simple polytope, whose proof is purely combinatorial. The talk is based on my latest work on the subject.