Thank you, modxers! With one small addition this is the perfect search script for me.
Due to the international flavour

of my recent project I’ve added 4 lines of code to this snippet, that I borrowed from xyzvisual (see
http://modxcms.com/forums/index.php/topic,1254.0.html for details). This transformes the search string to handle the german umlaute.
The changes: Search for "// CONFIGURE " (without quotation marks) and replace this with
// CONFIGURE
// Multilanguage Hack by xyzvizual
// see http://modxcms.com/forums/index.php/topic,1254.msg16206.html#msg16206
// if you need other character update this arrays
$umlaute = array("ä","ö","ü","Ä","Ö","Ü","&","ß");
$replace = array("ä","ö","ü","Ä","Ö","Ü","&","ß"); then do a search for "// End cleansing search string" and add the second part:
} // End cleansing search string
// Multilanguage search
$searchString = str_replace($umlaute, $replace, $searchString);
That does the job for me. Maybe other people find it useful.