one must change to the module directory and find the myModuleNameModule.php file and add the following (into the function init()):
$file = Yii::getPathOfAlias('myModuleName').DIRECTORY_SEPARATOR."further_directory_structure";
$url = Yii::app()->getAssetManager()->publish($file);
$cs = Yii::app()->getClientScript();
$cs->registerCssFile($url);
now the css-file is reachable from all views within this module.