  Given an origami (square-tiled surface) M with automorphism group G, we
compute the decomposition of the first homology group of M into isotypic
G-submodules. Through the action of the affine group of M on the homology
group, we deduce some consequences for the multiplicities of the Lyapunov
exponents of the Kontsevich-Zorich cocycle. We also construct and study several
families of interesting origamis illustrating our results.
