Sorry to have been a bit slow off the mark in replying to your question.
The classic role of HLA-B27 is (in combination with beta2-microglobulin) to present short peptides from intracellular pathogens for recognition by the T cell receptor of CD8 T-cells. B27 can also be expressed as cell surface beta2-microglobluin free homodimers. In addition to binding to the TCR, MHC class I molecules can also bind to immunoglobulin-like receptors (KIR). Natural Killer (NK) cells and some T-cells expressing the immune receptor KIR3DL2 can bind to B27 homodimers and are known to be expanded in B27+ AS patients.
The paper quoted put the hypothesis that ERAP1 allotypes form three functional groups; “normal”, “hypo-” or “hyper-” trimmers of peptides and that the prevalence of different ERAP1 allotype combinations has been shown to be different between AS cases and controls. This idea that low or high ERAP1 trimming activity might lead to the restricted supply of optimal peptides has the effect of unifying the mechanisms of homodimer formation and activation of innate and/or Th17 cells through the engagement KIR3DL2 receptors.
It is postulated that sub-optimal peptides (B27-ligands) generated by aberrant ERAP1 activity are able to bind with B27 sufficiently to pass intracellular quality control but that they may dissociate rapidly at the cell surface leading to increased levels of aberrant forms of B27. The authors were not able to rule out the possibility that different ERAP1 variants could generate specific arthritogenic peptides - so long story short - the question of unfolded protein response in the ER Vs cell surface B27 homodimers Vs arthritogenic peptide - remains unresolved.