Context
So I've been part of a very tight group of friends for more than a year now, and it feels like we're gonna be friends for a good while. We're all from 18 to 20 years old, and it's a mix of males and females (I'm a 20 y/o male). In that group there's a girl that tends to lie from time to time.
Exemples
Her : "I carried a friend to her boyfriend in 15 minutes". Which in that case is clearly impossible since it takes at least 45 minutes to travel that distance at 120km/h, so to do that in 15 min she would need to be driving at 300+ km/h. I know it's not a big deal but the problem is that when she lies to us, we all know she's lying and it's weirding us out and we don't know how to react and it gets kind of awkward.
Another problem is that nobody feels like contradicting her because she really looks like she believes herself. In the scenario that I told you we had the proof that it wasn't possible, but in most other cases we don't, but it still feels pretty obvious that she's lying. Furthermore, she'll lie in situations where she could be honest and it would be just fine. Example, her, two other friends (from that group of friends) and I had planned to go to another friend's house after we spent the day the together. The day comes along like planned and at the end of the day she looked tired and exhausted and I had the feeling she wouldn't want to come with us to our friend's house which would've been fine if she just told us she was too tired to come since it wasn't a party or anything that could make someone disappointed if she didn't come. But instead of saying the truth she started pretending she was losing her voice and she wanted to go home. Since she's a pretty bad liar we had doubts it was true, and we had our doubts confirmed when she "forgot to fake" as she started to talk normally for a few words and then noticed and went back to faking (didn't have the usual sound of someone losing their voice). So yet again it's no big deal, but it can get very irritating, and as we are very close friends we're expecting honesty from each other.
Additional Information
She can be stubborn when she wants to, she will most likely understand it as if I want to insult her rather than just try to fix an issue.
Her and I are very close to each other and are still getting closer with time. We have said to each other we would be interested to have a relationship in a not so far future, so being rude is not an option.
Aside from that issue she's a great person and everybody in our group appreciates her.
Question
I know that I could have a conversation with her about this or I could just tell her I don't believe her when I feel deceived so she'll start paying more attention to what she says. I want to talk to her to get her to stop lying all of the time. How can I do this without insulting her?