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We study 4D N=2 superconformal theories that arise from the compactificationof 6D N=(2,0) theories of type A_{2N-1} on a Riemann surface C, in the presenceof punctures twisted by a Z_2 outer automorphism. We describe how to do acomplete classification of these SCFTs in terms of three-punctured spheres andcylinders, which we do explicitly for A_3, and provide tables of properties oftwisted defects up through A_9. We find atypical degenerations of Riemannsurfaces that do not lead to weakly-coupled gauge groups, but to a gaugecoupling pinned at a point in the interior of moduli space.  As applications, we study: i) 6D representations of 4D superconformal quiversin the shape of an affine/non-affine D_n Dynkin diagram, ii) S-duality of SU(4)and Sp(2) gauge theories with various combinations of fundamental andantisymmetric matter, and iii) realizations of all rank-one SCFTs predicted byArgyres and Wittig.

Gaiotto Duality for the Twisted A_{2N-1} Series