Unique expectations for discrete crossed products

Let $G$ be a discrete group acting on a unital $C^{\ast }$-algebra $\mathcal{A}$ by $\ast$-automorphisms. We characterize (in terms of the dynamics) when the inclusion $\mathcal{A}\subseteq \mathcal{A}{⋊}_{r}G$ has a unique conditional expectation, and when it has a unique pseudo-expectation (in the sense of Pitts). Likewise for the inclusion $$\mathcal{A}$ \subseteq $\mathcal{A}$ \rtimes G$. As an application, we (slightly) strengthen results of Kishimoto and Archbold-Spielberg concerning $C^{\ast }$-simplicity of $$\mathcal{A}$ \rtimes_r G$.