When facing a difficult problem and trying to project confidence, I prefer sitting astride a rearing horse, brandishing a sabre.

The body language mirroring and influence thing has a comprehensive theory on using it to your advantage: Neuro-Linguistic Programming. Unfortunately, it has little experimental support, but it's still trendy with the management and life coaches--which doesn't necessarily make it not true; which wouldn't necessarily make it not useful.

This wasn't about trying to project confidence. It was a study that looked at students working alone. I find I will sometimes cross my arms if I am thinking hard about a problem. What was interesting was that the study provided some evidence that it would help me to persevere.