Amenability and Approximation Properties for Partial Actions and Fell Bundles

Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions Fell bundles over discrete groups. We prove that cross-sectional C*-algebra a bundle is nuclear if only underlying unit fibre AD-amenable. If action globalisable, then it AD-amenable its globalisation Moreover, preserved (weak) equivalence and, using very recent idea Ozawa Suzuki, show AD-amenabity equivalent to an approximation property introduced Exel.