Dynamical quantum groups at roots of 1

Given a dynamical twist for a finite-dimensional Hopf algebra, we construct two weak Hopf algebras, using methods of P. Xu and of P. Etingof and A. Va rchenko, and we show that they are dual to each other We generalize the the ory of dynamical quantum groups to the case when the quantum parameter q is a root of unity. These objects turn out to be self-dual-which is a fundame ntally new property, not satisfied by the usual Drinfeld-Jimbo quantum grou ps.