  Given a finite dimensional C-*-Hopf algebra H and its dual H^ we construct
the infinite crossed product A=... x H x H^ x H x ... and study its
representations. A is the observable algebra of a generalized spin model with
H-order and H^-disorder symmetries. By pointing out that A possesses a certain
compressibility property we can classify all DHR-sectors of A --- relative to
some Haag dual vacuum representation --- and prove that their symmetry is
described by the Drinfeld double D(H). Complete, irreducible, translation
covariant field algebra extensions F > A are shown to be in one-to-one
correspondence with cohomology classes of 2-cocycles u in D(H) @ D(H).
