This is a question on geometric tilting theory. On smooth projective variety it is possible to define in general tilting object as perfect complex that satisfy some properties, but are there examples of tilting objects that are actually complexes? All examples I know are vector bundles obtained as sums of exceptional sequences. What would be examples of different nature?
Edit: if we denote variety $X$ then tilting object $T$ in $D(X)$ is a perfect complex (or from the point of view of abstract triangulated categories "compact object") such that $T$ generates $D(X)$ and $Ext^i(T,T)=0$ for $i \neq 0$.