Classification of saturated Fell bundles: The discrete case and beyond

We present a classification framework for saturated Fell bundles over groups, utilizing data associated with their base group and unit fiber. This framework provides a unified perspective on the structure and properties of such bundles and yields key insights into their classification. In the case of discrete groups, we obtain a complete and transparent classification in terms of generalized factor systems, leading to a cohomological description of equivalence classes. For general locally compact groups, the situation is more delicate: While our construction extends to this setting, the classification depends on choices of topology on the underlying Banach bundle.