What are some of the key organizational elements that can affect the development and maintenance of a supportive organizational culture? As a consultant, what advice would you give to a functional org

What are some of the key organizational elements that can affect the development and maintenance of a supportive organizational culture? As a consultant, what advice would you give to a functional organization that was seeking to move from an old, adversarial culture, where the various departments actively resisted helping one another, to one that encourages "project thinking" and cross-functional cooperation?