Graded quasi-Baer $\ast$-ring characterization of Steinberg algebras

Given a graded ample, Hausdorff groupoid $G$, and an involutive field $K$, we consider the Steinberg algebra $A_K(G)$. We obtain necessary and sufficient conditions on $G$ under which the annihilator of any graded ideal of $A_K(G)$ is generated by a homogeneous projection. This property is called graded quasi-Baer $\ast$. We use the Steinberg algebra model to characterize graded quasi-Baer $\ast$ Leavitt path algebras.