  Double coset spaces of adelic points on linear algebraic groups arise in the
study of global fields; e.g., concerning local-global principles and torsors. A
different type of double coset space plays a role in the study of semi-global
fields such as p-adic function fields. This paper relates the two, by
establishing adelic double coset spaces over semi-global fields; relating them
to local-global principles and torsors; and providing explicit examples.
