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\large \bf Abstract
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We present a study of the decay $B^- \to D^0_{(CP)}K^-$ and its charge
conjugate, where $D^0_{(CP)}$ is reconstructed in both a non-$CP$
flavor eigenstate and in $CP$ ($CP$-even and $CP$-odd) eigenstates, based
on a sample of 382 million $\Upsilon{(4S)} \to B \overline{B}$ decays collected with the
BABAR detector at the PEP-II $e^+e^-$ storage ring. We measure the
direct $CP$ asymmetries $A_{CP\pm}$ and the ratios of the branching
fractions $R_{CP\pm}$:
$A_{CP+} = 0.27\pm 0.09\mathrm{(stat)}\pm 0.04\mathrm{(syst)}$,
$A_{CP-} =-0.09\pm 0.09\mathrm{(stat)}\pm 0.02\mathrm{(syst)}$,
$R_{CP+} = 1.06\pm 0.10\mathrm{(stat)}\pm 0.05\mathrm{(syst)}$,
$R_{CP-} = 1.03\pm 0.10\mathrm{(stat)}\pm 0.05\mathrm{(syst)}$.
These results will help to better constrain the gamma phase parameter
of the Cabibbo-Kobayashi-Maskawa quark mixing matrix.
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