Rigid dualizing complexes of affine Hecke algebras

We identify the rigid dualizing complex of the (generic) affine Hecke algebra $H_q$ attached to a reduced root system and deduce some structural properties as a consequence. For example, we show that the classical Hecke algebra $H_{q^{\pm }}$ as well as $H_q\mathrm{/}q$ are, under a certain condition on the root system, Frobenius over their centers with Nakayama automorphism given by an explicit involution.