  We show that a A-linear map of Hilbert A-modules is induced by a unitary
Hilbert module operator if and only if it extends to an ordinary unitary on
appropriately defined enveloping Hilbert spaces. Applications to the theory of
multiplicative unitaries compute the equivalence classes of Hilbert modules
over a class of C*- algebraic quantum groups. We thus develop a theory that for
example could be used to show non-existence of certain co-actions. In
particular, we show that the Cuntz semigroup functor takes a co-action to a
multiplicative action.
