  We present a method based on mutations of helices which leads to the
construction (in the large volume limit) of exceptional coherent sheaves
associated with the $(\sum_al_a=0)$ orbits in Gepner models. This is explicitly
verified for a few examples including some cases where the ambient weighted
projective space has singularities not inherited by the Calabi-Yau
hypersurface. The method is based on two conjectures which lead to the
analog,in the general case, of the Beilinson quiver for $\BP^n$. We discuss how
one recovers the McKay quiver using the gauged linear sigma model (GLSM) near
the orbifold or Gepner point in K\"ahler moduli space.
