One problem related to manifold/header/muffler/tail pipe has been reported for the 2001 Hyundai Santa Fe. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2001 Hyundai Santa Fe based on all problems reported for the 2001 Santa Fe.
Exhaust manifold cracked about 6 inches right down the middle. Discovered when car had about 42,000 miles. Original owner. I believe this could potentially be a fire hazard.