Consider the reduced crossed product $C(X)\rtimes_rG$. Let $\varphi$ be a positive linear functional on $C(X)\rtimes_rG$. Define the function $\phi: G \to C(X)^*$ by $\phi(g)(f)=\varphi(f\lambda_g),g \in G$ and $f \in C(X)$. Since $\varphi$ is a linear functional, $\phi$ is well-defined. Moreover...