  This note extends some recent results on the derived category of a geometric
invariant theory quotient to the setting of derived algebraic geometry. Our
main result is a structure theorem for the derived category of a derived local
quotient stack which admits a stratification of the kind arising in geometric
invariant theory. The use of derived algebraic geometry leads to results with
pleasingly few hypotheses, even when the stack is not smooth. Using the same
methods, we establish a "virtual non-abelian localization theorem" which is a
K-theoretic analog of the virtual localization theorem in cohomology.
