Moduli stack of principal bundles

In algebraic geometry, given a smooth projective curve X over a finite field ${\displaystyle \mathbf {F} _{q}}$ and a smooth affine group scheme G over it, the moduli stack of principal bundles over X, denoted by ${\displaystyle \operatorname {Bun} _{G}(X)}$, is an algebraic stack given by: for any ${\displaystyle \mathbf {F} _{q}}$-algebra R,

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