In this paper we consider K(n)~*(G), the Morava K-theory of certain Lie groups. Specifically, we compute K(n)~*(G) for G = G_2, F_4, E_6, E_7, E_8, PE_7 and PSp(m) at the prime 2, and PE_6 and PU(m) for odd primes. In particular, together with [Ho], [Y2] (see also [Hu]) and certain elementary observations, this completes the computations of the Morava K-theory of all the connected, simple, simply connected compact Lie groups with the sole exception the groups Spin(m) at the prime 2.
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