  We propose a new class of non-factorising D-branes in the product group GxG
where the fluxes and metrics on the two factors do not necessarily coincide.
They generalise the maximally symmetric permutation branes which are known to
exist when the fluxes agree, but break the symmetry down to the diagonal
current algebra in the generic case. Evidence for the existence of these branes
comes from a Lagrangian description for the open string world-sheet and from
effective Dirac-Born-Infeld theory. We state the geometry, gauge fields and, in
the case of SU(2)xSU(2), tensions and partial results on the open string
spectrum. In the latter case the generalised permutation branes provide a
natural and complete explanation for the charges predicted by K-theory
including their torsion.
