Algebraic Characters of Harish-Chandra Modules

We give a cohomological treatment of a character theory for (g, K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g, K) -modules. Due to results of Hecht, Schmid and Vogan the classical results of Harish-Chandra's global character theory extend to this general setting. As an application we consider a general setup, for which we show that algebraic characters answer discretely decomposable branching problems.