  We have performed the calculations for the nonleptonic $\Xi_b^- \rightarrow
\pi^- \ \Xi_c^0 (2790) \left(J=\frac{1}{2}\right)$ and $\Xi_b^- \rightarrow
\pi^- \ \Xi_c^0 (2815) \left(J=\frac{3}{2}\right)$ and the same reactions
replacing the $\pi^-$ by a $D_s^-$. At the same time we evaluate the
semileptonic rates for $\Xi_b^- \rightarrow \bar{\nu}_l l \ \Xi_c^0 (2790)$ and
$\Xi_b^- \rightarrow \bar{\nu}_l l \ \Xi_c^0 (2815)$. We look at the reactions
from the perspective that the $\Xi_c^0 (2790)$ and $\Xi_c^0 (2815)$ resonances
are dynamically generated from the pseudoscalar-baryon and vector-baryon
interactions. We evaluate ratios of the rates of these reactions and make
predictions that can be tested in future experiments. We also find that the
results are rather sensitive to the coupling of the $\Xi_c^*$ resonances to the
$D^* \Sigma$ and $D^* \Lambda$ components.
