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Let $G$ be a group acting on a finite left or right rigid monoidaltriangulated category ${\mathbf K}$ which has a Noetherian Balmer spectrum. Weprove that the Balmer spectrum of the crossed product category of ${\mathbf K}$by $G$ is homeomorphic to the space of $G$-prime ideals of ${\mathbf K}$, givea concrete description of this space, and classify the $G$-invariant thickideals of ${\mathbf K}$.

Group actions on monoidal triangulated categories and Balmer spectra