  We investigate the relation between the algebraic construction of boundary
states in AdS_3 and the target space analysis of D-branes and show the
consistency of the two descriptions. We compute, in the semiclassical regime,
the overlap of a localized closed string state with boundary states and
identify the latter with D-branes wrapping conjugacy classes in AdS_3. The
string partition function on the disk is shown to reproduce the spacetime DBI
action. Other consistency checks are performed. We also comment on the role of
the spectral flow symmetry of the underlying SL(2,R)/U(1) coset model in
constructing D-branes that correspond to degenerate representations of SL(2,R).
