The Tate spectrum of the higher real K-theories at height n=p-1

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Let Eₙ be Morava E-theory and let G ⊂ Gₙ be a finite subgroup of Gₙ, the extended Morava stabilizer group. Let EₙtG be the Tate spectrum, defined as the cofiber of the norm map N:(Eₙ)hG → EₙhG. We use the Tate spectral sequence to calculate π*Eₚ₋₁tG for G a maximal finite p-subgroup, and p an odd prime. We show that Eₚ₋₁tG ≃, so that the norm map gives equivalence between homotopy fixed point and homotopy orbit spectra. Our methods also give a calculation of π*Eₚ₋₁hG, which is a folklore calculation of Hopkins and Miller.