I now used the orignal .htaccess of q2a installation, only uncommenting the RewriteBase, still the same index.php redirect problem.
Digging into qa-index.php I see that question mark is to be found here:
$questionpos=strpos($origpath, '?');
and the "index.php" might be added by this line:
$urlformat=( (empty($_SERVER['REQUEST_URI'])) || (strpos($_SERVER['REQUEST_URI'], '/index.php')!==false) )
Could this be the problem? But why is it working with the other forums? Different Apache settings?
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Probably an Apache decoding problem!