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We present a study of the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}_{(CP)}^{0}{K}^{\ensuremath{-}}$ and its charge conjugate, where ${D}_{(CP)}^{0}$ is reconstructed in $CP$-even, $CP$-odd, and non-$CP$ flavor eigenstates, based on a sample of $232\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\mathit{\ensuremath{\Upsilon}}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ storage ring. We measure the partial-rate charge asymmetries ${A}_{CP\ifmmode\pm\else\textpm\fi{}}$ and …