  In 2008, the author proposed a version of duality theory for (not
necessarily, Abelian) complex Lie groups, based on the idea of using the
Arens-Michael envelope of topological algebra and having an advantage over
existing theories in that the enclosing category in it consists of Hopf
algebras in the classical sense. Recently these results were refined and
corrected by O.Yu.Aristov. In this paper, we propose a generalization of this
theory to the class of (not necessarily Abelian) countable discrete groups.
