Low GPA, what to do?

First off, you will not have to calculate your GPA into the American standard 4.0 system. Chances are, your 6.83 is better than your perceived 2.7/4. AdComs know the rigor and the grading system and will make the necessary adjustments.

Second off, a high GMAT will always somehow compensate for a lower GPA. Now, a "high" GMAT is quite subjective, but if I were you, I'd aim as high as I can get (aim for 800 and settle for what you get). Having said that, not everyone will be able to get 760 or 770, such as myself. If that were the case, an alternative transcript is always a good thing to think about if you have the time. If you're gearing for round 2 applications, an alternative transcript is not going to work. Take several business-oriented courses via some extension courses online or community colleges - get A's! If you're able to do that, you're showing the AdComs your seriousness in getting this MBA, and the ability to succeed in each school's MBA program. Last, but not least, you can always improve your candidacy by displaying leadership ability in and outside of work. This is something that you should probably have already; if not, it's never too late to start. All of these combined will most likely land you, at least an interview, if not an acceptance.