  We give the beginnings of the development of a theory of what we call
"R-coactions" of a locally compact group on a $C^*$-algebra. These are the
coactions taking values in the maximal tensor product, as originally proposed
by Raeburn. We show that the theory has some gaps as compared to the more
familiar theory of standard coactions. However, we indicate how we needed to
develop some of the basic properties of R-coactions as a tool in our program
involving the use of coaction functors in the study of the Baum-Connes
conjecture.
