Cartan subalgebras in uniform Roe algebras

In this paper we study structural and uniqueness questions for Cartan
subalgebras of uniform Roe algebras. We characterise when an inclusion
$B\subseteq A$ of $\mathrm{C}^*$-algebras is isomorphic to the canonical
inclusion of $\ell^\infty(X)$ inside a uniform Roe algebra $C^*_u(X)$
associated to a metric space of bounded geometry. We obtain uniqueness results
for `Roe Cartans' inside uniform Roe algebras up to automorphism when $X$
coarsely embeds into Hilbert space, and up to inner automorphism when $X$ has
property A.