The Hao-Ng isomorphism theorem for reduced crossed products

We prove the Hao-Ng isomorphism for reduced crossed products by locally compact Hausdorff groups. More precisely, for a non-degenerate $\mathrm{C}^*$-correspondence $X$ and a generalized gauge action $G \curvearrowright X$ by a locally compact Hausdorff group $G$, we prove the commutation ${\mathcal