A generalization of the cuntz algebras and multiplicative unitaries

A Cuntz algebra OH is associated functorially with an infinite-dimensional Hilbert space H. It is a simple C∗-algebra distinct from the algebra O∞, introduced by Cuntz. Generalizing ideas of Cuntz, the C∗-subalgebra generated by the intertwiners between tensor powers of a unitary representation on H of a multiplicative unitary in the sense of Baaj and Skandalis is considered. Partial answers are given to the following questions: When does this subalgebra have a trivial relative commutant? When does it coincide with the fixed-point algebra defined by the unitary representation? Is it isomorphic to OH in the case of the regular representation?