In this paper we extend work on exotic two-dimensional (2,[Formula: see text]2) supersymmetric gauged linear sigma models (GLSMs) in which, for example, geometries arise via nonperturbative effects, to (0,[Formula: see text]2) theories, and in so doing find some novel (0,[Formula: see text]2) GLSM phenomena. For one example, we describe examples in which bundles are constructed physically as cohomologies of short complexes involving torsion sheaves, a novel effect not previously seen in (0,[Formula: see text]2) GLSMs. We also describe examples related by RG flow in which the physical realizations of the bundles are related by quasi-isomorphism, analogous to the physical realization of quasi-isomorphisms in D-branes and derived categories, but novel in (0,[Formula: see text]2) GLSMs. Finally, we also discuss (0,[Formula: see text]2) deformations in various duality frames of other examples.