  We use an Adams spectral sequence to calculate the R-motivic stable homotopy
groups after inverting eta. The first step is to apply a Bockstein spectral
sequence in order to obtain h_1-inverted R-motivic Ext groups, which serve as
the input to the eta-inverted R-motivic Adams spectral sequence. The second
step is to analyze Adams differentials. The final answer is that the
Milnor-Witt (4k-1)-stem has order 2^{u+1}, where u is the 2-adic valuation of
4k. This answer is reminiscent of the classical image of J. We also explore
some of the Toda bracket structure of the eta-inverted R-motivic stable
homotopy groups.
