On the Semantic Web, objects can be identified by URIs and described by using RDF. With more and more RDF data published, object search on the Semantic Web is in demand for browsing, reuse, and integration. We developed the Falcons system, a keyword-based search engine for the Semantic Web. In this paper, we present the object search service provided by Falcons. For building an inverted index from query terms to Semantic Web objects (SW objects), we present a method to construct comprehensive textual description of SW objects. Furthermore, SW objects are also indexed from their classes and ancestor classes to support the class-based query restriction. Especially, class subsumption reasoning on multiple vocabularies on the Semantic Web is performed, and a class recommendation technique is proposed to enable hierarchically navigating classes. In addition, a summarization method for SW objects is devised to enable users to browse the summaries of objects.