We are talking about a warranty-related claim, not a claim about damages they'd have to pay regardless of the warranty offered. But anyway: If I travel outside

We are talking about a warranty-related claim, not a claim about damages they'd have to pay regardless of the warranty offered. But anyway: If I travel outside the US and buy a harmful appliance in a local shop, a US court would probably not take the case. Am I right? What would the manufacturer have to do to get exposure to US law?