We show that the bounded derived category of many singular projectve varieties (with isolated singularities) does not admit tilting objects (and more generally no semiorthogonal decompositions of "Kawamata-type“). Using singularity categories, most of our obstructions come from cluster theory via NCCRs and also from negative K-theory. Our approach is inspired by recent work of Kawamata. This is joint work with N.Pavic and E.Shinder.