It appears it searches the site with www.google.com : this could be explicitly mentioned.

Also, there is encrypted.google.com if we consider a search engine is synonym of Google. I've been told there are other pertinent search engines on the market. I've been told as well that Adobe's PDF Reader is not the only PDF reader on the market. I've also been told that several video formats can be read in Firefox without Adobe's Flash ...

What I mean is that this trend to name a famous, the most famous tool, be it for a file format or for a search engine, to call this tool systematically as if it were obvious is a bit misleading.

At least, please, make it clear to what search engine is used!

This very add-on, with a choice of search engines (similar add-ons exist already here on AMO) would bring it to the top in its category. But one search engine, moreover not explicitly stated, is really, IMO, excessively elementary.