It's a bit weird to explain, but this is the general story behind the Helmut/Prada/Theory thing:
Back in 1997, Helmut Lang launched "Helmut Lang Jeans", a lower-priced line that was a licensing deal with GTR Group. The diffusion line, which mostly consisted of high margin basics, became the cash cow for the label. The following year, Helmut Lang moved his headquarters and shows to New York.
In 1999, Prada acquired 51% of the Helmut Lang label. Under Bertezelli, the label went through intense restructuring, shifting to the operations of a more "traditional" luxury brand. This included axing the "Jeans" line in favour of using Helmut Lang's mainline collections as marketing vehicles to sell leather goods and perfumes. They also moved the shows back to Paris to further push that traditional luxury image.
Helmut Lang's customer base didn't respond to that vision, so the label's sales plummeted during the early '00s and Lang sold the remaining 49% of the label, before jumping ship in 2005. Prada sold the label to Link Theory in 2006, who relaunched the label as a contemporary label the following year.