In this paper, we study the subspace-dynamics of the operator $R_{g, v}(f):= E^{\mathcal{A}}(v f*\delta_g)$ on $L^p(\mathcal{B})$, $1\le p<\infty$. For an aperiodic element $g\in G$, we give the necessary and sufficient conditions on which $R_{g, v}$ is subspace-hypercyclic for $L^p(\mathcal{A})$ and $L^p(\mathcal{A}_D)$. The subspace-mixing of $R_{g, v}$ is also studied.
