  A study of $\Lambda_b^0$ baryon decays to the $DpK^-$ final state is
presented based on a proton-proton collision data sample corresponding to an
integrated luminosity of 9 fb$^{-1}$ collected with the LHCb detector. Two
$\Lambda_b^0$ decays are considered, $\Lambda_b^0\to DpK^-$ with $D\to
K^-\pi^+$ and $D\to K^+\pi^-$, where $D$ represents a superposition of $D^0$
and $\overline{D}^0$ states. The latter process is expected to be suppressed
relative to the former, and is observed for the first time. The ratio of
branching fractions of the two decays is measured, and the $C\!P$ asymmetry of
the suppressed mode, which is sensitive to the CKM angle $\gamma$, is also
reported.
