Project is a bit different than Outlook as it is not time zone aware. Consider these two scenarios for a solution.
1. Everyone uses the same calendar – Zulu Time. Work periods for resources are established in Zulu Time on resource calendars.
Set the project calendar to 24 hours.
Tasks are worked in the calendars assigned by their resource availability.
2. Use a 24 hour schedule. Purchase a small clock and set it on the wall to mark the time you want to use as the "project time zone". Workers enter their time, etc. based on the clock on the wall. Simple, and it works.
3. Same as 1 and 2, but use the time zone where most of the resources exist, or where the PMO may exist.