  We show that the superconformal symmetries of the (1,1) sigma model decompose
into a set of more refined symmetries when the target space admits projectors
$P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with
respect to the two natural torsionful connections $\nabla^{(\pm)}$ that arise
in the sigma model. Surprisingly the new symmetries still close to form copies
of the superconformal algebra, even when the projectors are not integrable, so
one is able to define a superconformal theory not associated with a particular
geometry, but rather with non-integrable projectors living on a larger
manifold. We show that this notion of non-geometry encompasses the locally
non-geometric examples that arise in the T-duality inspired doubled
formulations, with the benefit that it is more generally applicable, as it does
not depend on the existence of isometries, or invariant structures beyond
$P_{\pm}$ and $Q_{\pm}$. We derive the conditions for (2,2) supersymmetry in
the projective sense, thus extending the relation between (2,2) theories and
bi-Hermitian target spaces to the non-geometric setting. In the bosonic
subsector we propose a BRST type approach to defining the physical degrees of
freedom in the non-geometric scenario.
