(transitive) to give up on (one's efforts) / (reflexive) to give up / (transitive) to abandon, to forsake, to relinquish / (transitive, military) to surrender, to capitulate / (transitive) to lose hope, to resign, to quit / (transitive, mail) to send, to mail / (transitive, homework) to give

(idiomatic) to give up the ghost

present participle of aufgeben