  Using the relation between D-brane charges and K-theory, we study non-BPS
D-branes and their behavior under T-duality. We point out that in general
compactifications, D-brane charges are classified by relative K-theory groups.
T-duality is found to act as a symmetry between the relative K-theory groups in
Type II and Type I/IA theories. We also study Type \tilde\IA theory (which
contains an O8^- plane and an O8^+ plane), using K-theory and T-duality to
identify its stable D-branes. Comparison with string theory constructions
reveals two interesting effects. One of them involves the transfer of branes
between O-planes, while in the other, a D-brane charge which seems conserved
near one O-plane in fact decays due to the presence of another type of O-plane.
