My question relates to mesira. When is one allowed, under what circumstances, to go to the non-jewish authorities, if another jew is stealing/cheating/lying and causing significant financial harm to other jewish people and lying to the authorities about it (public company)?
Under certain circumstances it is permitted to go to the authorities. This is true in particular of cases where there is no other option by which to save oneself from harm. In the words of the Rosh (concerning going to secular courts), “If you call your fellow, and he refuses to come, thrown down a wall upon him!”
However, each case is of course different, and the correct course of action is to go first to Beis Din, and to receive a permit from Beis Din to go to the courts or to the relevant authorities.
Note that according to the Aruch Ha-Shulchan and others, the concept of mesira does not have the same sting in countries with a fair judicial system as it did in countries where a person was at the mercy of the whims of the authorities. Please see here for a previous related post.