2 problems

Bass trace conjecture for groupoids. The image of $D_0$ is contained in the direct summand

Let $K$ be a field, let $\mathcal{G}$ be an ample groupoid, and let $u\in\mathcal{G}^{(0)}$. Write $A_K(\mathcal{G})$ for the Steinberg algebra, $\mathcal{G}_u$ for the isotropy gr…