  We show that the derived category of coherent sheaves on the quotient stack
of the affine plane by a finite small subgroup of the general linear group is
obtained from the derived category of coherent sheaves on the minimal
resolution by adding a semiorthogonal summand with a full exceptional
collection. The proof is based on an explicit construction in the abelian case,
together with the analysis of the behavior of the derived categories of
coherent sheaves under root constructions.
