Global HRM means expanded and multi-work needs to be completed rather than HRM. Normally, when a company grows up in one country, HRM main role is to support with the recruitment, training, compensation and benefits, etc.
When the company grows to global or multinational company, GHRM also needs to allocate their skills person to the other countries. This is such a important role of GHRM as they should follow the local cultures, including allocating the staffs into the right places, handling all the internal and external issues, mix-cultures, etc.