CONJUGATION IN REPRESENTATION CATEGORIES OF MULTIPLICATIVE UNITARIES AND THEIR ACTIONS ON C-ASTERISK-ALGEBRAS

A conjugation functor f on a full subcategory of R(V), the representat ion category of a multiplicative unitary V, is defined. If V has a con jugate, it is also regular and the domain of f is all R( V). Examples of selfconjugate multiplicative unitaries are discussed. A coaction of the Hopf C-algebra associated with V on the Cuntz algebra O-d is can onically defined by a unitary object W of R(V) acting on a n-dimension al Hilbert space. As in the group action case if d = infinity and W be longs to the domain of f, ergodic coactions are often characterized by the absence of finite dimensional subreprzsentations of W. Furthermor e model actions of compact quantum group duals on C-algebras are defi ned. (C) 1996 Academic Press, Inc.