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We study the interplay between two nontrivial boundary effects: (1) the d-1 dimensional edge states of d-dimensional strongly interacting symmetry protected topological states, and (2) the boundary fluctuations of d-dimensional bulk quantum criticality. We also discuss states localized at an interface in a higher dimensional bulk, when the bulk undergoes a quantum phase transition. Using controlled analytical methods, we demonstrate that the interplay between the two different boundary effects leads to rich physics at the d-1 dimensional boundary, including new stable fixed points, and also an exotic quantum phase transition which cannot happen in a local d-1 dimensional system alone. Our analytical calculation is qualitatively consistent with recent numerical works on nonlocal quantum many body systems.