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MR947799 (89g:55027) 55R25 (55N20 55P42)
Rudyak, Yu. B. On the orientability of spherical, topological and piecewise linear bundles in complex $K$-theory. (Russian) Dokl. Akad. Nauk SSSR 298 (1988), no. 6, 1338--1341; translation in Soviet Math. Dokl. 37 (1988), no. 1, 283--286
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