  We study D-branes of the ${SL(2,\bR)}$ WZW model, and of its discrete
orbifolds. Gluing the currents by group automorphisms leads to three types of
D-branes: two-dimensional hyperbolic planes ($H_2$), de Sitter branes (dS$_2$),
or anti-de-Sitter branes (AdS$_2$). We explain that the dS$_2$ branes are
unphysical, because the electric field on their worldvolume is supercritical.
By combining ${SL(2,\bR)}$ and SU(2), we exhibit a class of supersymmetric
AdS$_2\times S^2$ three-brane worldvolumes, and consider their possible
embeddings in the near-horizon region of stringy black holes. We point out the
intriguing difference between the induced and the effective geometries of these
D-branes, and speculate on its possible significance.
