If your GET value contains a legitimate ticker code then this would work.
$rss->load('http://feeds.finance.yahoo.com/rss/2.0/headline?s='.$_GET['quote'].'®ion=US&lang=en-USsto');
You are already in a php context so is not the way to concatenate a string
This is however not a robust way to handle it as there is no checking that $_GET['quote'] is set or has any value, you would need to decide what to get if it was not set
UPDATE
NB the original URL given in the question is invalid
http://feeds.finance.yahoo.com/rss/2.0/headline?s=GOOG®ion=US&lang=en-USsto
does not work but
http://feeds.finance.yahoo.com/rss/2.0/headline?s=GOOG®ion=US&lang=en-US
does
So please update your code to
$rss->load('http://feeds.finance.yahoo.com/rss/2.0/headline?s='.$_GET['quote'].'®ion=US&lang=en-US');