Kevin, there are a few things you need to realize about the UP
First, you are from "away". There is no respect for you right now, so keep your stuff on high alert. Even in Houghton/Hancock, which is slightly more progressive due to MTU being there, people aren't going to give you a lot of respect.
Second, yes there isn't a lot in law enforcement, and people LIKE IT THAT WAY! Only a handful of Staties, some local, and the Woodscops. That's it, and it isn't bad. You need to be your own cop: talk to these kids (if they are under 18, have coffee with the parents at the Kalieva) and talk about your saw. But don't just jump into it. You need to build ties in this community, and right now, you are not coming across right. More than likely, the parents don't know where it came from, and you will get it back (and the kids will get their a$$ whooped for being a thief, unless they are scumbag parents, then your hosed anyways). This is a group of people who are fiercely independent, and you are still a potential "threat" (see the first comment). If I park on the side of the road in MN, I get a cop pulling up behind me in 15 minutes wanting to know WTF I am doing. (Seriously, happened just last week. Told me I can't be there, even though it was the side of the road in the middle of nowhere, and not on an Interstate).
Third, why the hell did you move TO the Yoop? I lived there for 23 years, and had to leave 12 years ago because I wanted to actually have a job that paid something. Sure, you can buy a house for $80K, but when you make $10/hr, it just isn't worth it. Granted, it is an outdoor wonderland, but you gotta eat. If I ever get financially "free", I would move back, but I can't count on that place to make a buck (just hunt them).
My $0.02
Shane