Carrot or the stick

I went to a speaker who was crazy for wanting to go to Iraq on his own free will and choice but even crazier to do it as a freelancer. He spewed a lot of leftist stuff which was kind of interesting but got old. He then got to the good stuff right before time ran out. He talked about the Romans who were masters of invading a place and being able to stay there and maintain it. What the Romans did in England was form an alliance with people that they were fighting. They built them a temple and named it jointly after a roman god and a local god and the fighting ceased. They used a carrot instead of a stick. This guy related an experience about a taxi ride. The driver said that ya everyone hated Saddam and then pointed to 12 giant cranes building a billion dollar US embassy. The Americans are viewed as the new overlords. Instead of using a stick what does a carrot look like in Iraq? Is it as simple as building a mosque? The US is seen as this Christian country fighting against a Muslim country. How do we embrace Islam in a way that creates peace?