In general US citizens and GC holders are subject to US federal income tax taxation, whether or not they actually live in the US.
However - there are two organizations in the world that provide an exemption to this rule for Green Card holders working outside the US: IMF and the World Bank:
Your work for an international organization and the international organization agreement creating the international organization provides that alien employees are exempt from U.S. income tax. Two international organizations that have such a provision are the International Monetary Fund (IMF) and the International Bank for Reconstruction and Development (World Bank).