Derivations in group algebra bimodules

If one introduces a norm in a group algebra which is understood as a vector space and considers a closure over this norm, a natural structure of a free bimodule over a group ring arises. The most natural example is $\ell_p(G)$, for $p \geq 1$. This structure makes it natural to consider the problem of describing derivations with values in such bimodules, which I will talk about. A "character" approach will be used, which consists in identifying the derivations with characters on a suitable category (in our case, the groupoid of adjoint action of a group on itself), and further study is already underway with the active use of combinatorial methods.