  Monotone operator theory and fixed point theory for nonexpansive mappings are
central areas in modern nonlinear analysis and optimization. Although these
areas are fairly well developed, almost all examples published are based on
subdifferential operators, linear relations, or combinations thereof.
  In this paper, we construct an intriguing maximally monotone operator induced
by a certain nonexpansive retraction. We analyze this operator, which does not
appear to be assembled from subdifferential operators or linear relations, in
some detail. Particular emphasis is placed on duality and strong monotonicity.
