Let \(\pi:X\twoheadrightarrow Y\) be an equicontinuous extension of compact Hausdorff \(G\)-spaces and let \(C(X), C(Y)\) be commutative and unital (or just commutative and nuclear?).

We assume that the map

\begin{equation}\label{eqn:assumed} (\ell^\infty(G) \otimes C(Y)) \rtimes_{\max}G \to \ell^\infty(G,C(Y)^{**})\rtimes_{\max} G \end{equation}

is injective.