Affine Deligne–Lusztig varieties via the doubleBruhat graph, II : Iwahori–Hecke algebra

We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties.This second part of a two-paper series uses this new language, i.e., the double Bruhat graph, to describe certain structure constants of the Iwahori-Hecke algebra.As an application, we describe nonemptiness and dimension of affine Deligne-Lusztig varieties for most elements of the affine Weyl group and arbitrary -conjugacy classes.