Adverbs

(r)offensivelyin an unpleasantly offensive manner“he smelled offensively unwashed”
(r)offensively, objectionably, obnoxiouslyin an obnoxious manner“he said so in one of his more offensively intellectually arrogant sentences”
(r)offensivelyaggressively“`In this crisis, we must act offensively,' the President said”, “the admiral intends to act offensively in the Mediterranean”