  We compute Ext-groups between classical exponential functors (i.e. symmetric,
exterior or divided powers) and their Frobenius twists. Our method relies on
bar constructions, and bridges these Ext-groups with the homology of
Eilenberg-Mac Lane Spaces.
  Together with the article "Troesch complexes and the twisting spectral
sequence" (arXiv 1005.3133), this article provides an alternative approach to
classical Ext-computations in the category of strict polynomial functors over
fields. We also obtain significant Ext-computations for strict polynomial
functors over the integers.
