  We discuss how gerbes may be used to set up a consistent Lagrangian approach
to the WZW models with boundary. The approach permits to study in detail
possible boundary conditions that restrict the values of the fields on the
worldsheet boundary to brane submanifolds in the target group. Such
submanifolds are equipped with an additional geometric structure that is
summarized in the notion of a gerbe module and includes a twisted Chan-Paton
gauge field. Using the geometric approach, we present a complete classification
of the branes that conserve the diagonal current-algebra symmetry in the WZW
models with simple, compact but not necessarily simply connected target groups.
Such symmetric branes are supported by a discrete series of conjugacy classes
in the target group and may carry Abelian or non-Abelian twisted gauge fields.
The latter situation occurs for the conjugacy classes with fundamental group
Z_2\times Z_2 in SO(4n)/Z_2. The branes supported by such conjugacy classes
have to be equipped with a projectively flat twisted U(2) gauge field in one of
the two possible WZW models differing by discrete torsion. We show how the
geometric description of branes leads to explicit formulae for the boundary
partition functions and boundary operator product coefficients in the WZW
models with non-simply connected target groups.
