* Καινοτομέω (kainotomeō): This is probably the closest single word. It literally means "to make something new" and is often used in modern Greek to mean "to innovate."
* Words emphasizing creation or invention: Words like εφεύρω (epheuro) (to invent), δημιουργώ (dimiourgo) (to create), or νεωτερίζω (neoterizo) (to modernize) could be used depending on the context. They capture aspects of innovation, but not the entire meaning.
The best choice would depend on the specific context. If you're writing something formal, using a phrase might be more precise than a single word. For instance, "εφαρμογή καινοτόμων ιδεών" (application of innovative ideas) conveys the meaning effectively.