  We generalize, explain and simplify Langer's results concerning Frobenius
direct images of line bundles on quadrics, describing explicitly the
decompositions of higher Frobenius push-forwards of arithmetically
Cohen-Macaulay bundles into indecomposables, with an additional emphasis on the
case of characteristic two. These results are applied to check which Frobenius
push-forwards of the structure sheaf are tilting.
