In this talk, I will explain how to construct a Topological Quantum Field Theory to compute virtual classes of character stacks in the Grothendieck ring of stacks. This construction extends the work of González-Prieto, Logares and Muñoz. I will also show a few features of the construction focusing on a couple of simple examples including the affine linear group of rank 1 and the semi-direct product of the multiplicative group G_m with the finite group of order 2. The work is joint with Jesse Vogel and Ángel González-Prieto.