He was completely 'oblivious of' [='unaware of'] the fact that he'd offended them.
We called out to them, but they remained 'oblivious'. [=they did not notice us]
She kept dancing, 'oblivious to' everyone around her.
(..) Just... I'm really... not great to be around, so - try not to get on my nerves. - Oh yeah. Hey, I've had a few girlfriends. I'm not completely oblivious! - You won't even know I'm here. - Okay. Oh! This is working right... The afternoon is so great! Look at that! So smooth! (..)2006 TvShow: The IT Crowd Title: Aunt Irma Visits Season: 1 Episode 6