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Dec 2, 2013 at 4:42 comment added Adam Hughes Sorry, Filippo, I was a bit incomplete. What I meant was $G$ acts on the $B_p$p--which are homogeneous spaces for $G$ (since the action is continuous and transitive)--so the action is basically just left-multiplication of the cosets $G/H_v$ where $H_v$ is the stabilizer of any $v$ (a place of $\overline{\mathbb{Q}}$ over $p$) since $B_p$ is topologically isomorphic to $G/H_v$ for any $v|p$ of $\overline{\mathbb{Q}}$.
Sep 13, 2012 at 3:20 history answered Filippo Alberto Edoardo CC BY-SA 3.0