K-THEORY FOR REAL C*-ALGEBRAS VIA UNITARY ELEMENTS WITH SYMMETRIES, PART II - NATURAL TRANSFORMATIONS AND KO*(R)-MODULE OPERATIONS

We extend the unitary picture of K-theory for real C*-algebras developed in an earlier paper by Terry Loring and the author, finding formulas for the KO* and KU* natural transformations in terms of this picture. In addition we study several examples, including suspension algebras and dimension drop algebras, finding unitary elements to represent all non-trivial elements of KOi(A).