On some $p$-approximation properties of discrete groups and $\ell^p$ uniform Roe algebras

We study $p$-approximation properties of $\ell^p$ uniform Roe algebras and their connections to coarse geometry and group theory. For bounded geometry metric spaces, property A implies $p$-nuclearity of $B_u^p(X)$ for $1<p<\infty$, while $B_u^1(X)$ is always $1$-nuclear. Property A also yields coeff