International teams tick when roles are clearly defined and when these roles are well understood by the team members
Structure the work processes more specifically and spell out more clearly what you are trying to achieve. That is how you get people in diverse teams get the work done.
This aspect is much more essential than establishing a clear goal. Why is that? Because in an international team role ambiguity can easily trigger cross-cultural confusion and allow team members to waste enormous amounts of time and energy. In addition, leaving the path to the goal somewhat open is likely to trigger increased ownership on how to reach the goal. The good fellas at Harvard Business Review put it this way:
Collaboration improves when the roles of individual team members are clearly defined and well understood—when individuals feel that they can do a significant portion of their work independently. Without such clarity, team members are likely to waste too much energy negotiating roles or protecting turf, rather than focus on the task.
In addition, team members are more likely to want to collaborate if the path to achieving the team’s goal is left somewhat ambiguous. If a team perceives the task as one that requires creativity, where the approach is not yet well known or predefined, its members are more likely to invest time and energy in collaboration. (Lynda Graton and Tamara J. Erickson, Eight ways to build collaborative teams, Harvard Business Review, Nov 2007.)
Thus, allow your international team to spend some more time and receive more advice on the need for better structured work processes as well as convincing them about the usefulness of continuously evaluating their collaboration culture.