Bronson Lim, Alexander Polishchuk: Bondal-Orlov fully faithfulness criterion for Deligne-Mumford stacks gives a (no surprises there, given the title) fully faithfulness criterion for functors originating in the derived category of a Deligne–Mumford stack. There is now a role to be played by the automorphism groups of a point, so that one needs to suitable improve the condition to be checked.
It'll be fun to find applications of this!
Marcello Bernardara, Sara Durighetto: A categorical invariant for geometrically rational surfaces with a conic bundle structure shows how to define a Griffiths–Kuznetsov component in the derived category of a conic bundle (although it is not quite a uniquely defined subcategory, rather a direct sum of them, i.e. considered motivically).
Gregorio Baldi: Some remarks on motivical and derived invariants is an interesting overview of conjectural derived invariants, and how the implications between them go.
In the light of the previously mentioned shift in the belief that Hodge numbers are not a derived invariant (also known as Kontsevich's conjecture), one sees that this would disprove Orlov's conjecture.