A new Frobenius exact structure on the category of complexes
  Let $(1)$ be an automorphism on an additive category $\mathcal{B}$, and let $\eta\colon (1)\to {\rm Id}_{\mathcal{B}}$ be a natural transformation satisfying $\eta_{X(1)}=\eta_X(1)$ for any object $X$ in $\mathcal{B}$. We construct a new Frobenius exact structure on the category of complexes in $\mathcal{B}$, which is associated to the natural transformation $\eta$. As a consequence, the category introduced in Definition 2.4 of [J. Rickard, Morita theory for derived categories, J. London Math. Soc. 39(1989), 436-456] has a Frobenius exact structure. 
Yan-Fu Ben, Yan-Hong Bao, Xian-Neng Du
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