Although Lutz was named GM's vice chairman for product development, Saab and Adam Opel AG product and design executives will report to their respective top executives, Saab CEO Peter Augustsson and Opel Chairman Carl-Peter Forster.
But Mike Burns, president of GM Europe, said Saab and Opel will receive "valuable counsel and input" from Lutz.
"It's good input, and some of it will take some discussion," Burns said in Frankfurt last week.
Lutz was scheduled to test drive Opels and competing models on Opel's test track last week, Burns said.
GM CEO Rick Wagoner said Lutz's focus will be in North America, where design, engineering and vehicle-line executives report directly to him. But Wagoner said GM is "not going to put a fence around Bob Lutz."