Projectivity of a faithfully balanced self-orthogonal bimodule

Question

Let $_RT_S$ be a faithully balanced self-orthogonal bimodule over a pair of noncommutative rings $(R,S)$, if $_RT$ is projective as a left $R$-module, can we say $T_S$ is also projective as a right $S$-module? $_RT_S$ is called a faithully balanced self-orthogonal bimodule provided that (1) $S$ $\cong$ $End(_RT)^{op}$ and $R$ $\cong$ $End(T_S)$ (2) $Ext^i_R(T,T)=0=Ext^i_S(T,T)$ for each $i>0$.