Let $R$ be a local Gorenstein ring. Let $\underline{\text{CM}}(R)$ be the stable category of maximal Cohen--Macaulay modules, it is known to carry a triangulated structure. My question is: If $M\to N\to L\rightsquigarrow$ is an exact triangle in $\underline{\text{CM}}(R)$, then does there exist an exact sequence $0\to M'\to N'\to L'\to 0$ in $\text{CM}(R)$ such that $M,N,L$ are projectively isomorphic with $M',N',L'$ respectively ?
