Large language models (LLMs) are being increasingly integrated into everyday products and services, such as coding tools and writing assistants. As these embedded AI applications are deployed globally, there is a growing concern that the AI models underlying these applications prioritize Western values. This paper investigates what happens when a Western-centric AI model provides writing suggestions to users from a different cultural background. We conducted a cross-cultural controlled experiment with 118 participants from India and the United States who completed culturally grounded writing tasks with and without AI suggestions. Our analysis reveals that AI provided greater efficiency gains for Americans compared to Indians. Moreover, AI suggestions led Indian participants to adopt Western writing styles, altering not just what is written but also how it is written. These findings show that Western-centric AI models homogenize writing toward Western norms, diminishing nuances that differentiate cultural expression.