  We present an ab-initio study of the Mn substitution for Ga in GaN using the
Heyd-Scuseria-Ernzerhof hybrid functional (HSE). Contrary to semi-local
functionals, the majority Mn t$_{2}$ manifold splits into an occupied doublet
and an unoccupied singlet well above the Fermi-level resulting in an insulating
groundstate, which is further stabilized by a sizeable Jahn-Teller distortion.
The predictions are confirmed using $GW$ calculations and are in agreement with
experiment. A transition from a localized to a delocalized Mn hole state is
predicted from GaN to GaAs.
