Measurement of $C\!P$ observables in the process $B^0 \to DK^{*0}$ with two- and four-body $D$ decays

Measurements of CP observables in B$^{0}$ → DK$^{∗0}$ decays are presented, where D represents a superposition of D$^{0}$ and $ {\overline{D}}^0 $ states. The D meson is reconstructed in the two-body final states K$^{+}$π$^{−}$, π$^{+}$K$^{−}$, K$^{+}$K$^{−}$ and π$^{+}$π$^{−}$, and, for the first time, in the fourbody final states K$^{+}$π$^{−}$π$^{+}$π$^{−}$, π$^{+}$K$^{−}$π$^{+}$π$^{−}$ and π$^{+}$π$^{−}$π$^{+}$π$^{−}$. The analysis uses a sample of neutral B mesons produced in proton-proton collisions, corresponding to an integrated luminosity of 1.0, 2.0 and 1.8 fb$^{−1}$ collected with the LHCb detector at centre-of-mass energies of $ \sqrt{s}=7,8 $ and 13 TeV, respectively. First observations of the decays B$^{0}$ → D(π$^{+}$K$^{−}$)K$^{∗0}$ and B$^{0}$ → D(π$^{+}$π$^{−}$π$^{+}$π$^{−}$)K$^{∗0}$ are obtained. The measured observables are interpreted in terms of the CP -violating weak phase γ.