Ten-dimensional IIB supergravity is invariant under the symmetry group SL(2.R). We give a classification of all the forms that are present in the IIB supersymmetry algebra as representations of SL(2,R), and we show under which conditions these forms are associated to branes whose effective actions are kappa symmetric. We use these results to give a simple universal SL(2,R)-invariant expression for all IIB brane actions.