This page describes how the Sortable-hosted CMP interacts with Google consent in order to deliver personalized or non-personalized ads.
The Sortable-hosted CMP shows a custom publisher purpose (with ID 1 and titled Google Personalisation) to which a user must consent in order to be served personalized Google ads. The purpose lists all Google ad technology providers that a publisher has enabled in their DFP. The user needs to provide consent in order to allow all the partners to display personalized Google ads. If a user does not consent to this purpose, non-personalized ads are shown to the user.
Here is an example of the CMP showing the custom publisher purpose: