The cylinder over the Koras-Russell cubic threefold has a trivial   Makar-Limanov invariant
  We show that the Makar-Limanov invariant of the cylinder over the Koras-Russell cubic affine threefold is trivial. This means that regular functions which are invariant under all algebraic actions of the additive group on this variety are constants. 
Adrien Dubouloz (IMB)