Residually finite partial actions and MF Fell bundles

Abstract

We study Blackadar and Kirchberg's matricial field (MF) property and quasidiagonality in cross-sectional $C^{⁎}$-algebras constructed from Fell bundles and, in particular, from partial $C^{⁎}$-dynamical systems. In doing so we generalize Kerr and Nowak's notion of a residually finite action to partial topological dynamical systems. We look at some examples exhibiting this property including the partial Bernoulli shift which produces an MF reduced crossed product provided the group in question is exact, residually finite, and admits an MF reduced group $C^{⁎}$-algebra.