  In this work we propose new non-commutative gauge theories that describe the
dynamics of branes localized along twisted conjugacy classes on group
manifolds. Our proposal is based on a careful analysis of the exact microscopic
solution and it generalizes the matrix models (`fuzzy gauge theories') that are
used to study e.g. the bound state formation of point-like branes in a curved
background. We also construct a large number of classical solutions and
interpret them in terms of condensation processes on branes localized along
twisted conjugacy classes.
