We propose a cross-lingual framework for fine-grained opinion mining using bitext projection. The only requirements are a running system in a source language and word-aligned parallel data. Our method projects opinion frames from the source to the target language, and then trains a system on the target language using the automatic annotations. Key to our approach is a novel dependency-based model for opinion mining, which we show, as a byproduct, to be on par with the current state of the art for English, while avoiding the need for integer programming or reranking. In cross-lingual mode (English to Portuguese), our approach compares favorably to a supervised system (with scarce labeled data), and to a delexicalized model trained using universal tags and bilingual word embeddings.