  A general form for the boundary coupling of a Lie algebroid Poisson sigma
model is proposed. The approach involves using the Batalin-Vilkovisky formalism
in the AKSZ geometrical version, to write a BRST-invariant coupling for a
representation up to homotopy of the target Lie algebroid or its subalgebroids.
These considerations lead to a conjectural description of topological D-branes
on generalized complex manifolds, which includes A-branes and B-branes as
special cases.
