What are the suggestions to improve cross functional coordination?

First and foremost, put someone in charge for accountability. The account manager, a project manager, a product manager or executive depending on the purpose of the coordination.

Next, create some team incentives (the carrot) and some penalties (the stick). If a team member is not cooperating or completing task in a timely manner, professionaly make them accounttable with the ultimate authority for the project. If the team player has a higher titile, the ultimate authority and accountality must be to an executive with the greatest title.

Conduct team building sessions, this can be as simple as getting together for lunch, dinner, beers or some social setting. We are social creatures, never under estimate the calue of team building.