Abstract
We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of `localized and transportable endomorphisms', which produce anyonic excitations from the ground state. Following the Doplicher--Haag--Roberts (DHR) sector theory from AQFT, we organize these endomorphisms into a braided monoidal category capturing the fusion and braiding properties of the anyons. We show that this category is equivalent to Rep_f D(G), the representation category of the quantum double of G. This establishes for the first time the full DHR structure for a class of 2d quantum lattice models with non-abelian anyons.