I would probably say "welcome to" our group, but "in" isn't exactly wrong. You could even say "into our group." It depends entirely what kind of feeling you want to convey. "To our group" is simple and straightforward, "in" is supposed to give the person who's welcomed a "homey" feeling, one of now being an intrinsic part of the group, and the same goes for "into."

"Welcome in" sounds like an incorrect Germanism to me. "Welcome to" works in ever situation I can think of, even if there are cases where "welcome in" or "into" might work.

Statt einer Regelangabe!
willkommen bei uns - welcome to our home (Du bist noch nicht eingetreten.)

You are welcome in our shop (Du stehst schon im Laden und wirst begrüßt.)
You are welcome in advance (schon im Voraus willk.)

As a "Sei Wilkommen" style exclamation, I'd go with "Welcome to" every time. "Welcome to our group." I would never use (as a speaker of AE) "in/into" in that sentence.

The indicative "We'd like to welcome you (in)to our group" is fine, but not "...welcome you in our group"--agree with RobNYNY that it sounds like a Verdeutschung.

"You are welcome here" is pretty rare, but correct. "I welcome you to my shop" or "you are welcome in my shop" is problematic on many levels: it's not a common practice among English-speaking cultures so, while technically correct, sounds like "foreigner-speak."

@HeDoMo: well, plenty of AE speaker say both "welcome in" and "into our group." Even Dave Barry (you might have heard of him) says it, and he's not exactly a lightweight among columnists.

http://blogs.herald.com/dave_barrys_blog/2007...
...that's exactly the kind of fresh perspective we need to stamp out before something gets accomplished nurture and welcome into our group ...

clarification:

yes, for use in the indicative...integrated in a sentence...you certainly introduce and welcome new concepts (things) into a group.

For the "ich heiße sie herzlich wilkommen" situations, RobNYNY and I feel "to" is about the only option.