We present a study of the decay B^- → D^0_(CP)K^±
and its charge conjugate, where D^0_CP) is reconstructed
in CP-even, CP-odd, and non-CP flavor eigenstates, based on a sample of 232 x 10^6 Y(4S) → BB decays
collected with the BABAR detector at the PEP-II e^+e^- storage ring. We measure the partial-rate charge
asymmetries A_(CP±) and the ratios R_(CP±) of the B → D^0K decay branching fractions as measured in CP^±
and non-CP D^0 decays: A_(CP±) 0:35 ± 0.13(stat) ± 0.04(syst), A_(CP-)= -0.06 ± 0.13(stat) ±
0.04(syst), R_(CP+) = 0.90 ± 0.12(stat) ± 0.049syst), and R_(CP-) = 0:86 ± 0.10(stat) ± 0.05(syst)
