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It is well known that symmetry protected topological (SPT) phases hostnon-trivial boundaries that cannot be mimicked in a lower-dimensional systemwith a conventional realization of symmetry. However, for SPT phases of bosons(fermions) within the cohomology (supercohomology) classification the boundarycan be recreated without the bulk at the cost of a non-onsite symmetry action.This raises the question: can one also mimic the boundaries of SPT phases whichlie outside the (super)cohomology classification? In this paper, we study thisquestion in the context of 2+1D fermion SPTs. We focus on the root SPT phasefor the symmetry group $G =Z_2 \times Z^f_2$. Starting with an exactly solvablemodel for the bulk of this phase constructed by Tarantino and Fidkowski, wederive an effective 1d lattice model for the boundary. Crucially, the Hilbertspace of this 1d model does not have a local tensor product structure, butrather is obtained by placing a local constraint on a local tensor productHilbert space. We derive the action of the $Z_2$ symmetry on this Hilbert spaceand find a simple 3-site Hamiltonian that respects this symmetry. We study thisHamiltonian numerically using exact diagonalization and DMRG and find strongevidence that it realizes an Ising CFT where the $Z_2$ symmetry acts as theKramers-Wannier duality; this is the expected stable gapless boundary state ofthe present SPT. A simple modification of our construction realizes theboundary of the 2+1D topological superconductor protected by time-reversalsymmetry ${\cal T}$ with ${\cal T}^2 = (-1)^{\cal F}$.

1d lattice models for the boundary of 2d "Majorana" fermion SPTs: Kramers-Wannier duality as an exact $Z_2$ symmetry