[fdr]

Inflation is (over a long enough time) embedded in stock price, since what you own is really a share of the production and assets of the firm you purchased a share in...it only happens to be denominated in dollars. If a firm you bought stock in is in the business of making shoes, and it is making a larger number of well-received shoes, regardless of the price level for shoes (and the price level of the stock), this kind of stock will generally appreciate in real terms.

In principle, the denominating currency does not matter: someone could give you some number of shoes for your share, and your dividends could likewise be in shoes. We tend to find it more convenient to work in dollars.