Do inverted nipples have a higher chance of breast sheet cancer?

Maybe. Inverted nipple or nipples may be long standing or of sudden onset. Those of sudden onset would be more worrying, especially if on one side. There are many benign causes of nipple inversion ( see http://en.Wikipedia.Org/wiki/inverted_nipple). However, breast cancer can cause distortion of the breast tissue and lead to nipple inversion. Inversion, especially unilateral, should be checked by doc.