Final answer:
Al-Shabaab is the terrorist group based in Somalia with the goal of creating a global Islamic caliphate, connected with Al-Qaeda and ISIS's extremism and global violence.
Step-by-step explanation:
The terrorist group headquartered in Somalia that aims to create a global Islamic caliphate is Al-Shabaab. Al-Shabaab is known for its violence and ties with the larger Al-Qaeda network, with the two groups sharing an extremist ideology and methods of terror, including self killing attacks and mass violence against civilians. Their goal is not only to establish control in Somalia but also to contribute to a global effort in the creation of a caliphate, a state governed by a Muslim leader with both religious and political authority over Muslims worldwide. This aligns with similar objectives by other extremist groups such as ISIS, which has caused devastation in Syria and Iraq.