  We prove a conjecture of Morel identifying Voevodsky's homotopy invariant
sheaves with transfers with spectra in the stable homotopy category which are
concentrated in degree zero for the homotopy t-structure and have a trivial
action of the Hopf map. This is done by relating these two kind of objects to
Rost's cycle modules. Applications to algebraic cobordism and construction of
cycle classes are given.
