My talk will focus on two-dimensional SU(N) gauge theories coupled to massless fermions in a real representation of the gauge group. I will use lattice regularization and overlap fermions and show that salient features known in the continuum are reproduced. I will focus on lattice gauge action with a twisted plaquette. Properties of zero modes for N=2 and fermions in the spin-one representation will be demonstrated on the lattice. Majorana-Weyl fermions will also be discussed and the associated ‘t Hooft vertex will be shown to factorize into chiral sectors. The resulting condensate is present in finite volume. The scale set by this condensate might not be connected to the presence/absence of a conformal sector in the infra-red.