Holomorphic duality for countable discrete groups

In 2008, the speaker introduced a version of duality theory for (not necessarily abelian) complex Lie groups. The idea was to use Arens-Michael envelopes of topological algebras. The advantage of this approach is that the ambient category consists of Hopf algebras in the classical sense. Recently these results were corrected and refined by O. Yu. Aristov. In the present talk, we discuss an extension of this theory to arbitrary (not necessarily abelian) countable discrete groups.