The étale Brauer-Manin obstruction is the only obstruction to strong approximation for the classifying stack BG of a linear algebraic group G over a number field k.
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The \'{e}tale Brauer-Manin obstruction for classifying stacks
The étale Brauer-Manin obstruction is the only obstruction to strong approximation for the classifying stack BG of a linear algebraic group G over a number field k.