The regular representation and regular covariant representation of crossed products of Woronowicz C*-algebras

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×αG correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C-algebra acted upon by a discrete group G.Meanwhile,it is also shown that the regular covariant C-algebra is the Woronowicz C-algebra which corresponds to a multiplicative unitary.Finally,an explicit description of the multiplicative unitary operator for C(SU（2） )×α（?） is given in terms of those of the Woronowicz C-algebra C(SU（2） ) and the discrete group G.