ACTIONS OF COMPACT QUANTUM GROUPS ON C-ASTERISK-ALGEBRAS

In this paper we investigate a structure of the fixed point algebra un der an action of compact matrix quantum group on a C-algebra B. We al so show that the categories of C-comodules in B and inner endomorphism s restricted to the fixed point algebra coincide when the relative com mutant of the fixed point algebra is trivial. Next we show a version o f the Tannaka duality theorem for twisted unitary groups.