The PM could influence the assigned resources via the following ways:
- Motivation - that their contribution is crucial for the successful completion of the project
- Remind them of the strategic/tactical value of the project to the organization
- Direct Authority - tactfully referencing to the project sponsor who has supposedly "bestowed" the PM with the power to hold the stick
- Indirect Authority - by having a good business relationship with the assigned resources' immediate bosses. This takes effort & some amount of goodwill from within the PM's other juridiction to them. This good relationship opens up a useful path for the PM to escalate issues regarding the resource.