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There's a hook called "generate_after_header" that you can hook in to.

If you have GP Hooks - you can add your HTML in the "After Header" hook.

This is a fonction only for pages, not ?

I would like a similary possibility for my "home page" (www.xyz.com) not for real page (www.xyz.com/generate).

Is't possible ?

I found a solution with GP Hooks / After Header, it works, but I can not aficher the image in the center, it is still left

Try to give a class for your image, and then use this code on your style.css file

IMG.yourclassname {
    display: block;
    margin-left: auto;
    margin-right: auto }

This should center your image.

The above CSS should work (thanks, Jean!).

You can also wrap the image in a container, like so:

<div class="grid-container grid-parent">
      Your image html in here.
</div>