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

The special McKay correspondence and exceptional collection