this paper, we deal with another approximation property, called local reflexivity ([@EffrosHaagerup Section 5]). It is much weaker than nuclearity. Because a weak expander sequence does not have property A, a uniform Roe algebra of a weak expander sequence is not nuclear. The goal of this paper is to show much stronger negation.

Let $X = \bigsqcup_{m = 1}^\infty X_m$ be a sequence of weak expander spaces. Then the uniform Roe algebra $C^*_\mathrm{u}(X)$ is not locally reflexive.

Since exactness implies local reflexivity [@KirchbergExactUHF], we have the following corollary.

A uniform Roe algebra of a sequence of expander graphs is not exact.

In Section \[SectionGenBox\], we prepare the notion of a generalized box space, which is a special kind of a coarse space. In Section \[SectionLocalReflexivity\], we review the definition of a uniform Roe algebras and local reflexivity of C$^*$-algebras. In Section \[SectionGroupoid\], we construct a topological groupoid associated to a coarse space. The groupoid is different from that in [@SkandalisTuYu]. Its topology is generated by countably many compact and open subsets. In Section \[SectionProof\], it is proved that the groupoid has an invariant measure, if the space is a generalized box space. If the uniform Roe algebra is locally reflexive, 