  We present a spectrum-level version of the norm map in equivariant homotopy
theory based on the algebraic construction in work of Greenleess-May. We show
that this new norm map is same as the construction in work Hill-Hopkins-Ravenel
on the Kervaire invariant problem. Our comparison of the two norm maps gives a
conceptual understanding of the choices inherent in the definition of the
multiplicative norm map.
