TITLE: Lindel's theorem for semisimple simply connected G
QUESTION [5 upvotes]: Let $k$ be a field.
$G/k$ be a simply connected semisimple algebraic group. 
Let $X/k$ be a smooth affine $k$-scheme. 
Question: Is every principal $G$ bundle on $X\times {\mathbb A}^1$ a pull back from $X$?

REPLY [3 votes]: You may also want to look at http://arxiv.org/abs/1308.3078. You will see that the answer is in general "no" even if you assume that $k$ is the field of complex numbers.