On some $p$-approximation properties of exact 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 a discrete metric space $X$ with bounded geometry, we prove that property A implies $p$-nuclearity of the $\ell^p$ uniform Roe algebra $B^p_u(X)$ for every $p\in(1,\i