To the downvoters: it is customary and polite to explain your reasons for downvoting a question. Perhaps you might like to leave suggestions for how the question could be improved.

Do you mean $B(i)$ rather than $I(j)$ in the superscript? And is $I=\lbrace 1, \dots, N \rbrace$?

Sebastian, I don't have a good enough understanding of the technical contents to answer your question, sorry. But I hope that the papers will be helpful to you.

I guess I should mention that Andre also has another paper called Quantum Functions that is concerned with similar notions.

@NicolaCiccoli Yes, I wouldn't suspect Baaj-Skandalis-Vaes to come up with a trivial notion! It just seems a funny way to phrase the definition - it makes more sense if $G$ is the focus of the definition rather than $G_1$ and $G_2$.

@TheUser yes, of course you're right.

I don't think that Wells proves the equivalence, but Chapter III, Section 2 does go into a lot of detail on such connections.

I think it means topological as opposed to measure-theoretic.