Google announced and update for AdSense for Search that enables you to host the search results directly on your own pages, unlike before, where you were redirected to a Google domain.
Publishers using AdSense for search now have the option to open search results within their own websites. By adding an additional set of search results code to your page, you can display Google search results framed within your own site. This new option will help you blend AdSense for search into your site even further. You'll also have the added advantage of keeping users on your site while still offering them the useful information available through Google search.
More details on the how to over here.
Want to see it in action, I set up a test page at https://www.seroundtable.com/adsense-search.html.