  The aim of this work is to present a general theory of coset models G/H in
which different left and right actions of H on G are gauged. Our main results
include a formula for their modular invariant partition function, the
construction of a large set of boundary states and a general description of the
corresponding brane geometries. The paper concludes with some explicit
applications to the base of the conifold and to the time-dependent Nappi-Witten
background.
