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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