Exceptional cycles in triangular matrix algebras

An exceptional cycle in a triangulated category with Serre functor is a generalization of a spherical object. Suppose that $A$ and $B$ are Gorenstein algebras, given a perfect exceptional $n$-cycle $E_{\ast }$ in $K^b(A\mbox{-}{\rm proj})$andaperfectexceptional$m$-cycle$F_$in$K^b(B\mbox{-}{\rm proj})$,weconstructan$A$-$B$-bimodule$N$,andprovetheproduct$E_\boxtimes F_*$isanexceptional$(n+m-1)$-cyclein$K^b(\Lambda\mbox{-}{\rm proj})$,where$\Lambda=\begin{pmatrix}A & N\ 0 & B \end{pmatrix}$. Using this construction, one gets many new exceptional cycles which is unknown before for certain class of algebras.