Given a dynamical twist for a finite dimensional Hopf algebra we construct
two weak Hopf algebras, using methods of Xu and Etingof-Varchenko, and show
that they are dual to each other. We generalize the theory 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 fundamentally new property, not
satisfied by the usual Drinfeld-Jimbo quantum groups.
