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

在Anantharaman-Delaroche（AD）先前的论文的基础上，我们介绍并研究了离散组中部分动作和Fell束的AD适应性的概念。我们证明，当且仅当下面的单位纤维是核且Fell束可适应AD时，Fell束的横截面\（C ^ * \）-代数才是有核的。如果部分动作是可全局化的，则且仅当其全球化可用于AD时，它才可用于AD。而且，我们证明Fell束的（弱）等价关系保留了AD适应性，并且使用Ozawa和Suzuki的最新思想，我们证明了AD适应性等效于Exel引入的近似性质。