This is joint work with Eric Friedlander, Julia Pevtsova and Andrei Suslin We consider modules over an elementary abelian group on which every element in the radical, but not the square of the radical, has the same Jordan canonical form. Such modules can be used to define bundles on projective spaces and Grassmanians. They have many interesting properties. We can get them as submodules of any module of the group algebra. In this talk I will discuss some of the constructions and their generalizations.