AMP pages displaying your own domain
Today we are rolling out support in Google Search’s AMP web results (also known as “blue links”) to link to signed exchanges, an emerging new feature of the web enabled by the IETF web packaging specification. We believe that privacy-preserving instant loading web content is a transformative user experience, but in order to accomplish this, we had to make trade-offs; namely, the URLs displayed in browser address bars begin with google.com/amp, as a consequence of being shown in the Google AMP Viewer, rather than display the domain of the publisher. We heard both user and publisher feedback over this, and last year we identified a web platform innovation that provides a solution that shows the content’s original URL while still retaining AMP’s instant loading.
Source: webmasters.googleblog.com