I have red and yellow bell peppers. As they have begun to ripen, the areas that start to change colors quickly become wrinkled and soft while the rest of the pepper remains firm and smooth.
Bell Pepper Wrinkling and Softening
Certified GKH Gardening Expert
I find this to be a common issue and complaint from many gardeners.
Generally it can be more of an environmental issue. Sun, water, temperatures all can effect the ripening time.
Generally if it is wrinkling it is overripe and should be picked before this happens.
I might suggest using Epsom Salt on the peppers. I have good luck in pepper production with the use of it.
I add it weekly to the plant throughout the growing season.
Here are some links for you.