  We systematically apply the formalism of duality walls to study the action of
duality transformations on boundary conditions and local and nonlocal operators
in two, three, and four-dimensional free field theories. In particular, we
construct a large class of D-branes for two-dimensional sigma-models with
toroidal targets and determine the action of the T-duality group on it. It is
manifest in this formalism that T-duality transformations on D-branes are given
by a differential-geometric version of the Fourier-Mukai transform.
