A matrix model for branes on WZW simple current orbifolds

Non-commutative geometry of D-brane worldvolumes on simple current orbifolds of WZW models of type AN is analysed within the framework of reflection equation algebras. Our study of a class of symmetries of the latter is shown to lead to an explicit construction of (fractional) quantum orbifold branes. The orbifolding procedure itself is given a straightforward algebraic realisation in the formalism developed. The ensuing orbifold matrix models are then demonstrated to yield results on brane tensions and the algebra of functions in agreement with the exact BCFT data.