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Boundary states for D-branes at orbifold fixed points are constructed inclose analogy with Cardy's derivation of consistent boundary states in RCFT.Comments are made on the interpretation of the various coefficients in theexplicit expressions, and the relation between fractional branes and wrappedbranes is investigated for $\mathbb{C}^2/\Gamma$ orbifolds. The boundary statesare generalised to theories with discrete torsion and a new check is performedon the relation between discrete torsion phases and projective representations.Comment: LaTeX2e, 50 pages, 5 figures. V3: final version to appear on JHEP  (part of a section moved to an appendix, titles of some references added, one  sentence in the introduction expanded

Orbifold boundary states from Cardy's condition