Looks like crepe or fresco to me, both of which tend to be pretty wrinkle-resistant. And local shop plus no wrinkles makes me think it's probably a poly and/or nylon blend -- not that there's anything wrong with that. Coolest suiting I've ever had was a wool, linen and nylon blend, from J. Crew, early-mid 90s.
In my opinion, it's not fresco, because the linen doesn't matches any of my own fresco characteristics (rough hand and made of wool). BTW, is Fresco a weave?
It is very possible that there's some synthetics blended in. However, it still is best summer (brazilian summer) fabric that I've ever worn. The greatest downside, for me, is that it doesn't have any body.