A C*-algebra is said to be nowhere scattered if it has no nonzero elementary ideal-quotients. It is known that the Global Glimm Property -a notion introduced by Kirchberg and Rørdam in their study of purely infinite C*-algebras- implies nowhere scatteredness. The Global Glimm Problem asks if the converse holds: Does every nowhere scattered C*-algebra have the Global Glimm Property?

I will explain how both the Global Glimm Property and nowhere scatteredness can be translated to divisibility properties in the Cuntz semigroup. This provides a new approach to the Global Glimm Problem, which can be used to obtain two conditions in the Cuntz semigroup that capture precisely what a nowhere scattered C*-algebra needs to have in order to satisfy the Global Glimm Property.