  Let $G$ be a discrete group acting on a unital $C^*$-algebra $\mathcal{A}$ by
$*$-automorphisms. In this note, we show that the inclusion $\mathcal{A}
\subseteq \mathcal{A} \rtimes_r G$ has the pure extension property (so that
every pure state on $\mathcal{A}$ extends uniquely to a pure state on
$\mathcal{A} \rtimes_r G$) if and only if $G$ acts freely on
$\mathcal{\widehat{A}}$, the spectrum of $\mathcal{A}$. The same
characterization holds for the inclusion $\mathcal{A} \subseteq \mathcal{A}
\rtimes G$. This generalizes what was already known for $\mathcal{A}$ abelian.
