You'll need to experiment with a few different things until you find the one that works... The first thing I'd probably try is:

...
binmode STDOUT, ":utf8";
print $webObject;
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Then of course you have to make sure you have an appropriate method for actually viewing the output -- a utf8-aware terminal window, a browser set to utf8 encoding, etc.

If that doesn't work, and you don't know what else to try, reply back with some more details (an actual url, what you are using to view the data, etc).

(update: sometimes it's hard to work out the logic of what is going wrong... another thing to try, if the above does not work, is:

use Encode;
...
$webObject = decode( "utf8", get( $URL ));
...
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If you try that without the "binmode" thing, you should get warnings about "wide character in print...", and doing binmode STDOUT,":utf8"; should make those warnings go away.)