  We answer the recent problem posed by Baudier, Braga, Farah, Vignati, and
Willett that asks whether the $\ell_\infty$-direct sum of the matrix algebras
embeds into the uniform Roe algebra or the quasi-local algebra of a uniformly
locally finite metric space. The answers are no and yes, respectively. Hence
the inclusion of the uniform Roe algebra into the quasi-local algebra can be
proper.
