Frobenius Push-Forwards on Quadrics

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.