Reduced cross-sectional algebra of an approximation-property Fell bundle over an inverse semigroup is exact iff its unit fiber is exact.
[BEM17] Alcides Buss, Ruy Exel, and Ralf Meyer
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Exactness and Fell bundles with the approximation property over inverse semigroups
Reduced cross-sectional algebra of an approximation-property Fell bundle over an inverse semigroup is exact iff its unit fiber is exact.