Hi,
To generate the content we give parameters to the Joomla function:
JHTML::_('select.'.$characteristic_display.'list', $this->values, $map, 'class="inputbox" size="1"' . $this->options, 'value', 'text', (int)$value,$id );
In the "display()" function of that file.
So what do you exactly want to do ?
You can potentially replace the line:
$html = JHTML::_('select.'.$characteristic_display.'list', $this->values, $map, 'class="inputbox" size="1"' . $this->options, 'value', 'text', (int)$value,$id );
to pass your custom html content in the $html var, or you can change the given informations to the current function.