Comments on D-branes on Orbifolds and K-theory

We systematically revisit the description of $D$-branes on orbifolds and the classification of their charges via K-theory. We include enough details to make the results accessible to both physicists and mathematicians interested in these topics. The minimally charged branes predicted by K-theory in Z_N orbifolds with $N$ odd are only BPS. We confirm this result using the boundary state formalism for Z_3. For Z_N x Z_N orbifolds with and without discrete torsion, we show that the K-theory classification of charges agrees with the boundary state approach, largely developed by Gaberdiel and collaborators, including the types of representation on the Chan-Paton factors.