Measurement of $B\to D^0 K^*$ decays with $D^0\to CP$ eigenstates

We use 384 million $\Upsilon(4S)\to B\bar{B}$ events collected with the BaBar detector at the PEP-II $B$ Factory to study the decay $B^-\to D^0 K^{*-}$ where the $K^{*-}\to K_S^0 \pi^-$ and the $D^0$ decays into $CP$-eigenstates. In particular, we reconstruct the $CP=+1$ final states into $K^+K^-$ and $\pi^+\pi^-$ and the $CP=-1$ final states into $K_S^0\pi^0$, $K_S^0\phi$, and $K_S^0\omega$. We also include the non-$CP$ mode $D^0\to K^-\pi^+$ in our study.