adverb (r)

• in an unpleasantly offensive manner(adv.all)

  Example:
  He smelled offensively unwashed.
  

  Antonym:
  inoffensively
  

  source: wordnet30
• in an obnoxious manner(adv.all)

  Example:
  He said so in one of his more offensively intellectually arrogant sentences.
  

  Synonym:
  objectionably, obnoxiously
  

  source: wordnet30
• in an aggressive manner(adv.all)

  Example:
  `In this crisis, we must act offensively,' the President said.
  The admiral intends to act offensively in the Mediterranean.
  

  Synonym:
  aggressively, sharply
  Antonym:
  defensively
  

  source: wordnet30