ag.algebraic geometry - Equivalence of derived categories which is not Fourier-Mukai

Schlichting gave an example of two categories of singularities which are derived equivalent but whose K-groups are not isomorphic. Dugger and Shipley (arXiv:0710.3070) expanded on this example and noted that it gives two dga's which are derived equivalent but not by an integral transform.

Otherwise, Lunts and Orlov's results on uniqueness of enhancements give a large class of triangulated categories for which one might lift exact functors to dg-functors and apply Toen's result.