What did Hermes invent according to Greek mythology which he traded with Apollo for cattle?

When Apollo found out that Hermes stole his cattle, he took Hermes to Zeus. Zeus was more amused than mad at Hermes. Hermes showed them his Lyre and started playing. Apollo became enchanted by the music and the song. The song flattered Apollo for his cleverness, nobility, and generosity. Apollo then offered to exchange his entire herd of cattle for the lyre. Hermes agreed, and a reconciliation between the brothers began. They returned to Olympus, where Zeus formally united them in friendship and fellowship as the story goes.

Next, Hermes became the god of herdsmen, whilst Apollo devoted himself very enthusiastically to the art of music. Also Hermes then swore to Apollo that he would never again steal any of his possessions. For this promise, Apollo gave Hermes Heralds golden staff, protective of wealth and prosperity, which became one of the symbols of Hermes. After that Hermes began building another musical instrument for his amusement: a reed-pipe.

Additionally with their (these two gods) reconciliation, Apollo promised Hermes that he would become the messenger of the gods. He and his mother would have renown among the immortals. So Hermes’ promise to his mother was finally fulfilled.

See: http://www.crystalinks.com/hermes2.html