  Heterotic toriodal Z2xZ2 orbifolds may possess discrete torsion between the
two defining orbifold twists in the form of additional cocycle factors in their
one-loop partition functions. Using Gauged Linear Sigma Models (GLSMs) the
consequences of discrete torsion can be uncovered when the orbifold is smoothed
out by switching on appropriate blowup modes. Here blowup modes with twisted
oscillator excitations are chosen to reproduce bundles that are close to the
standard embedding without torsion. The orbifold resolutions with discrete
torsion are distinguished from resolutions without torsion, since they require
NS5-branes at their exceptional cycles.
