Kahn-Priddy theorems via the norm

We revisit the Kahn-Priddy theorem from the perspective of modern equivariant homotopy theory. This allows for a short proof that may be applied in other settings with sufficiently robust analogues of multiplicative norms and the Adams isomorphism. We illustrate this by establishing new Kahn-Priddy theorems in $L_n$ and $L_n^f$-local homotopy theory, motivic homotopy theory, and synthetic homotopy theory.