I’m trying to create a custom actionBar with a different shape (not rectangular) as shown on the image below, does anyone knows point me on the right direction?

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At this point, it is no longer an ActionBar. Something like that would be a custom View.
It is missing a number of key components of the ActionBar such as the application icon and back arrow, and is lacking all of an ActionBar’s styling.
You can create a completely custom View class and use that, or make a reusable layout and include it wherever needed using an include tag.