Real Cobordism and Greek Letter Elements in the Geometric Chromatic Spectral Sequence

In a previous paper [5], the authors investigated extensively the Landweber-Araki Real cobordism spectrum MR ([1, 7]), and its stable summand at p = 2 called BPR. An Adams-like spectral sequence based on BPR was constructed, and homotopy groups of many spectra related to BPR were calculated. The goal of the present note is to begin investigating the question as to how BPR-theory contributes to the known information about stable homotopy groups of spheres. This question is not easy. The dimension to which stable stems have been calculated to date is, (if somewhat hazy), certainly high enough to make calculating past that point from scratch a substantial challenge for any new method. At this point, the authors did not get far enough in calculating with BPR to get any new information that way. On the other hand, any effort to compare the BPR-based spectral sequence with other known spectral sequences is frought with the usual difficulty: elements can get renamed.