Suppose $S$ is a scheme, and $G$ a smooth $S$-group scheme.
Then there exists an algebraic stack BG called the classifying stack of $G$, defined as the quotient stack $[S/G]$ where $G$ acts trivially on $S$. I was wondering what is $Pic(BG)$.
Is it true that $Pic(BG)= H^1(k,G)$ when $S=Speck$ the spectrum of a field?
What can we say in general?