Abstract
We give an easy proof that the Morava K-theories for BO(q) and MO(q) are in even degrees. Although this is a known result, it had followed from a difficult proof that BP^*(BO(q)) was Landweber flat. Landweber flatness follows from the even Morava K-theory. We go further and compute an explicit description of K(n)_*(BO(q)) and K(n)_*(MO(q)) and reconcile it with the purely algebraic construct from Landweber flatness.
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