I explain how the CAR algebra admits a Cantor spectrum C*-diagonal that is not conjugate to its standard AF diagonal. This is done by classification theory of stably finite nuclear C*-algebras, and the diagonal arises by realising the CAR algebra as the crossed product of a free and minimal action on the Cantor space, where the acting group is the product of a locally finite group with the infinite dihedral group. The main ingredient in the construction is a binary subshift associated to the well-known regular paper-folding sequence.
The resulting diagonal pair has finite diagonal dimension, and upon taking tensor products one obtains countable many Cantor spectrum diagonals which are pairwise non-conjugate.
This is joint work with Grigoris Kopsacheilis.
