Every connective spectrum with mod p homology in degrees divisible by 2p-2 has algebraic EO theory, yielding an EO-orientation for MY_{4p-4} and answering Hovey and Ravenel's question.
TransactionsoftheAmer- ican Mathematical Society, 357(1):129–150, 2005
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An Orientation Map for Height p-1 Real E Theory
Every connective spectrum with mod p homology in degrees divisible by 2p-2 has algebraic EO theory, yielding an EO-orientation for MY_{4p-4} and answering Hovey and Ravenel's question.