Proper triangular G(a)-actions on A(4) are translations

We describe the structure of geometric quotients for proper locally triangulable G(a)-actions on locally trivial A(3)-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X = 1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable G(a)-action on the affine four space A(k)(4) over a field of characteristic 0 is a translation with geometric quotient isomorphic to A(k)(3).