$QF$-proper classes and relative stable categories

A relative version of Rickard's theorem is proved, namely, if $\omega$ is a quasi-Frobenius proper class of short sequences in an Abelian category $\mathscr A$, then $\omega$-stable category of the category $\mathscr A$, is a quotient category of the relative bounded derived category $D^b_{\omega}(\mathscr A)$.