The reduced Hao-Ng isomorphism problem for non-degenerate product systems

We prove that the reduced Hao-Ng isomorphism problem has an affirmative answer for a generalised gauge action of a locally compact Hausdorff group on a non-degenerate product system over a unital subsemigroup of a discrete group.

In the possible absence of a faithful conditional expectation on the reduced crossed product, we employ the Plancherel weight and integrability of reduced coactions.

Using this approach, we establish that the identity representation of the induced product system inside the reduced crossed product of the Fock C*-algebra is Fock covariant.