Is it possible to map custom fields from the CRM to Projects?

When a Deal is won I would like to create a Project based on the Deal. I would like information from the Deal to be populated in the associated Project. If the data cannot be mapped is it possible to create Lookup fields in Projects with the CRM data?

Examples:

Deal: Providing a Training to a Company

Contact in Deals to Contact in Project

Date of Service in CRM to Date of Service in Projects