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This is true for $G=GL(r)$, as shown by Quillen and Suslin. For arbitrary $G$ there are counterexamples. Quite surprisingly, see even $G$-bundles over $\textrm{Spec }k$ may not be trivial. See the paper M. S. Raghunathan "Principal bundles on affine space and bundles on the projective line", Mathematische Annalen Volume 285, Number 2, 309-332 |
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This is true for $G=GL(r)$, as shown by Quillen and Suslin. For arbitrary $G$ there are counterexamples, see the paper M. S. Raghunathan "Principal bundles on affine space and bundles on the projective line", Mathematische Annalen Volume 285, Number 2, 309-332 |
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