  Using the Bockstein spectral sequence developed previously by the authors, we
compute the ring ER(n)^*(BO(q)) explicitly. We then use this calculation to
show that the ring spectrum MO[2^{n+1}] is ER(n)-orientable (but not
ER(n+1)-orientable), where MO[2^{n+1}] is defined as the Thom spectrum for the
self map of BO given by multiplication by 2^{n+1}.
