Picard groups of higher real K-theory spectra at height p - 1

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real -theory spectra of Hopkins and Miller at height , for an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra , where is Lubin-Tate -theory at the prime and height , and is any finite subgroup of the extended Morava stabilizer group. We find that these Picard groups are always cyclic, generated by the suspension.