I have started adding some references to

on modules ($C^\ast$-modules) of (continuous, etc..) convolution algebras of topological/Lie groupoids.

I still need to look into this more closely. A motivating question for this kind of thing is:

what’s the right fine-tuning of the definition of modules over twisted Lie groupoid convolution algebras such that for centrally extended Lie groupoids it becomes equivalent to the corresponding gerbe modules?

This seems fairly straightforward, but there are is some technical fine-tuning to deal with. I was hoping this is already stated cleanly in the literature somewhere. But maybe it is not. Or maybe I just haven’t seen it yet.

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