  Let $K/F$ be a finite extension of number fields and $S$ be a finite set of
primes of $F$, including all the archimedean ones. In this paper, using some
results of Gonz\'alez-Avil\'es \cite{Aviles}, we generalize the notions of the
relative P\'olya group $\Po(K/F)$ \cite{ChabertI,MR2} and the Ostrowski
quotient $\Ost(K/F)$ \cite{SRM} to their $S$-versions. Using this approach, we
obtain generalizations of some well-known results on the $S$-capitulation map,
including an $S$-version of Hilbert's theorem 94.
