admittedly; it is true (used to introduce a factor which is opposed to the main line of argument but is not regarded as so strong as to invalidate it)

granted, Marie was two years older than her, but it wasn't a question of age

even assuming that

granted that officers were used to making decisions, they still couldn't be expected to understand

agree to give or allow (something requested) to

they were granted a meeting

her request was granted

agree or admit to (someone) that (something) is true

he hasn't made much progress, I'll grant you that