What are the roles of PMO may play in your organization (Depending on your organizational structure)?

it is already answered,

the PMo can have a supporting role for PMs and also for teaching them.

plus it can follow the Organization goals achieving among with projects and programs.

To simply says, control the project for successful completion within the budget and duration.

The Project Management Office (PMO) is a centralized management structure for a group of projects in an organization, aimed at ensuring standardization, reducing duplication and leveraging resources such as people, technology, and communication

Not all organizations require the structure and discipline of a PMO, sometimes simply called a Project Office. Determining factors might be any combination of:

• available budget,
• number of concurrent projects,
• high percentage of failed projects,
• repeated project management issues,
• number of inexperienced project managers, and
• need for centralized project monitoring and control.

In addition, there are several organizational factors which, if in place, will accelerate acceptance of the guidance, coaching, monitoring, and project control afforded through a PMO.

• First, your organization’s sponsorship of the Project Management Office must be at the senior management level of your organization – either the CFO, CIO, or CTO should be your PMO Sponsor. Executive Leadership over the Project Management Office (someone directly involved in the day-to-day governance of PMO activities) might be a VP-Level (“VP, PMO” or “VP of Solutions Delivery” or “VP of Service Delivery” are recognized titles) and reporting to one of the C-Levels mentioned above.
• Second, your organization recognizes the need for a Project Management Office by providing adequate funding in the operational budget. Similar to an organization’s commitment to Quality by establishing a Quality group reporting to the CEO, establishing and funding a PMO team is evidence of an organization’s commitment to consistent project management discipline and control.
• Third, your organization’s senior leadership communicates an organization-wide commitment to project management discipline and success by implementing a structured project selection process; providing for project manager training and certification; and establishing criteria for successful project performance.
• Finally, the implementation of your PMO must be as a resource and support team for your individual project managers and project teams - not as another layer between projects and senior management.

Conclusion

The exact roles and responsibility of the PMO varies among organizations, depending on organizational needs and the nature of projects executed by the organization. A proper application of PMO nevertheless enables the organization to undertake quality work with lesser resources, lesser risk, and lesser costs.

thanks for invition ,,,,,,,,,, i agree with experts answers

I leave the answer to the experts, specialists in this field

Audit compliance with Project policies, standards, and procedures companywide 

• Help to provide project resources 

• Cancel projects 

• Provide templates and standardized forms for project use 

• Offer coaching, training and mentoring for project managers 

• Serve as a centralized communications conduit for projects 

• Manage dependencies between projects, programs, or portfolios 

• Function as a stakeholder